diff --git a/README.md b/README.md
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--- a/README.md
+++ b/README.md
@@ -1,24 +1,18 @@
-# Geometric and numerical methods in optimal control I
+# Geometric and numerical methods in optimal control II
-1. Optimal control of ODE's
-([video](https://pod.univ-cotedazur.fr/video/11163-geometric-and-numerical-methods-in-optimal-control-i-14))
+## Course
-2. Example: Goddard's problem ("fly high")
-([video](https://pod.univ-cotedazur.fr/video/11164-geometric-and-numerical-methods-in-optimal-control-i-24))
+* [Course](doc/course/simple_shooting_general.ipynb)
+* [Notes](doc/course/course.pdf)
-3. Refresher on Runge-Kutta methods
-([video](https://pod.univ-cotedazur.fr/video/11172-geometric-and-numerical-methods-in-optimal-control-i-34))
+## Exercices
-4. A "do it yourself" direct solver
-([video](https://pod.univ-cotedazur.fr/video/11173-geometric-and-numerical-methods-in-optimal-control-i-44))
+* [Application of the indirect simple shooting method](doc/exercices/simple_shooting_application.ipynb)
+* [Coding the indirect simple shooting method](doc/exercices/simple_shooting_coding.ipynb)
+* [Introduction to the multiple shooting method](doc/exercices/bsb_turnpike_regularized.ipynb)
-[Course notes](course/course.pdf)
-
-[Hands on 1](https://github.com/jump-dev/JuMPTutorials.jl/blob/master/notebook/modelling/rocket_control.ipynb)
-
-[Hands on 2](https://ct.gitlabpages.inria.fr/gallery/goddard/goddard.html)
[FAQ](https://optimalcontrol.zulip.beta.cimpa-lms.info/#narrow/stream/284-geometric_methods1)
@@ -26,15 +20,6 @@
[ct (control toolbox)](https://ct.gitlabpages.inria.fr/gallery)
-[Geometric and numerical methods in optimal control II](https://ct.gitlabpages.inria.fr/gallery/shooting_tutorials/simple_shooting_general)
-
-[Julia tutorial](https://syl1.gitbook.io/julia-language-a-concise-tutorial)
-
-[JuMP](https://mlubin.github.io/pdf/jump-sirev.pdf)
-
-Hager, W. W.; Hou, H.; Mohapatra, S.; Rao, A. V.; Wang, X.-S.
-[Convergence rate for a Radau hp collocation method applied to constrained optimal control](https://doi.org/10.1007/s10589-019-00100-1).
-*Computational Optimization and Applications* **74** (2019), 275-314
+[Geometric and numerical methods in optimal control I](https://gitlab.polytech.unice.fr/CIMPA/gnmoc)
-Hairer, E.; Lubich, C.; Wanner, G. *Geometric Numerical Integration*. Springer, 2006
diff --git a/doc/course/course.pdf b/doc/course/course.pdf
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@@ -0,0 +1,1550 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Generalities about the indirect simple shooting method\n",
+ "\n",
+ "* Author: Olivier Cots\n",
+ "* Date: March 2021\n",
+ "\n",
+ "------\n",
+ "\n",
+ "**_Abstract_**\n",
+ "\n",
+ "We present in this notebook the **indirect simple shooting** method based on the [Pontryagin Maximum Principle (PMP)](https://en.wikipedia.org/wiki/Pontryagin%27s_maximum_principle) to solve a smooth optimal control problem. By smooth, we mean that the maximization condition of the PMP gives a control law in feedback form (i.e. with respect to the state and the costate) at least [continuously differentiable](https://en.wikipedia.org/wiki/Smoothness#Differentiability_classes).\n",
+ "\n",
+ "We use the [nutopy](https://ct.gitlabpages.inria.fr/nutopy/) package to solve the optimal control problem by simple shooting. You can find another smooth example with more details about the use of nutopy at this [page](https://ct.gitlabpages.inria.fr/gallery/smooth_case/smooth_case.html): note that in this example, the nutopy package is interoperated with the [bocop](https://ct.gitlabpages.inria.fr/bocop3/) software, implementing a direct collocation method.\n",
+ "\n",
+ "**_Goal_**\n",
+ "\n",
+ "The goal of this presentation is that at the end, you will be able to implement an indirect simple shooting method with nutopy package on an academic optimal control problem for which the optimal control (that is the solution of the problem) is smooth. We assume you have some basic knowledge on optimal control theory. To achieve the goal, you can start by simply read the text and the code at the end of the notebook. For a deeper understanding and more details, you can watch the videos embedded in the notebook. All these videos explain the material you can find here: [pdf file](https://gitlab.inria.fr/ct/gallery/-/raw/master/examples/shooting_tutorials/lecture.pdf).\n",
+ "\n",
+ "**_Contents_**\n",
+ "\n",
+ "* I) Statement of the optimal control problem and necessary conditions of optimality\n",
+ " * a) Definition of the optimal control problem - [Video](https://youtu.be/QUbeyLNZR8A)\n",
+ " * b) Application of the Pontryagin Maximum Principle - [Video](https://youtu.be/xedLNn08Kn4)\n",
+ " * c) The hidden true Hamiltonian - [Video](https://youtu.be/inCRJZWT3Ng)\n",
+ " * d) Illustration of the resolution of the necessary conditions of optimality - [Video](https://youtu.be/oRm8_Grs2Aw)\n",
+ "* II) Examples and boundary value problems\n",
+ " * a) Simple 1D example - [Video](https://youtu.be/r4oYTkF76TA)\n",
+ " * b) Calculus of variations - [Video](https://youtu.be/Ud16jTQbsQ0)\n",
+ " * c) An energy min navigation problem\n",
+ "* III) Indirect simple shooting\n",
+ " * a) The shooting equation - [Video](https://youtu.be/YVG2Z_TEkBQ)\n",
+ " * b) The iteration of the Newton solver and the Jacobian of the shooting function - [Video](https://youtu.be/hVbi9kShR90)\n",
+ " * c) A word on the Lagrange multiplier - [Video](https://youtu.be/3VEi-UHAS6w)\n",
+ "* IV) Numerical resolution of the shooting equations with the nutopy package\n",
+ " * a) Simple 1D example\n",
+ " * b) Calculus of variations\n",
+ " * c) An energy min navigation problem - exercice\n",
+ " \n",
+ "[thumbnail](simple_shooting.png)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## I) Statement of the optimal control problem and necessary conditions of optimality"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### a) Definition of the optimal control problem\n",
+ "\n",
+ "We consider the following smooth (all the data are at least $C^1$) *Optimal Control Problem* (OCP) in Lagrange form, with fixed initial condition and final time:\n",
+ "\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\int_0^{t_f} L(x(t),u(t)) \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = f(x(t),u(t)), \\quad u(t) \\in U, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = x_0 , \\quad c(x(t_f)) = 0_{\\mathrm{R}^k},\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "with $U \\subset \\mathrm{R}^m$ an arbitrary control set and with $c$ a smooth application such that its Jacobian $c'(x)$ (or $J_c(x)$) is of full rank for any $x$ satisfying the constraint $c(x)=0$. The solution $u$ belongs to the *set of control laws* $L^\\infty([0, t_f], \\mathrm{R}^m)$.\n",
+ "\n",
+ "<!-- <video width=600 src=\"https://www.youtube.com/embed/26EYyWlKjXc\" controls> Definition of the OCP</video> -->"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"640\"\n",
+ " height=\"360\"\n",
+ " src=\"https://www.youtube.com/embed/QUbeyLNZR8A\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x104742fd0>"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.display import IFrame\n",
+ "IFrame(\"https://www.youtube.com/embed/QUbeyLNZR8A\", width=640, height=360)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### b) Application of the Pontryagin Maximum Principle\n",
+ "\n",
+ "Let us denote by\n",
+ "$$\n",
+ " H(x,p,u) := p \\, f(x,u) + p^0\\, L(x,u),\n",
+ "$$\n",
+ "\n",
+ "the *pseudo-Hamiltonian* (that is the non-maximized Hamiltonian) associated to the optimal control problem.\n",
+ "\n",
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Pontryagin Maximum Principle_**\n",
+ " \n",
+ "According to the PMP, if $u$ is solution of the problem (with $x$ the *associated trajectory*), then there exists a *covector* $p$ (which is [absolutely continuous](https://en.wikipedia.org/wiki/Absolute_continuity)), a scalar $p^0 \\in \\{-1, 0\\}$, a *Lagrange multiplier* $\\lambda$, such that: \n",
+ "\n",
+ "\n",
+ "1. $(p, p^0) \\ne (0,0)$,\n",
+ "\n",
+ "2. $\\displaystyle \\dot{x}(t) = \\nabla_p H(x(t),p(t),u(t))$, $\\displaystyle \\dot{p}(t) = -\\nabla_x H(x(t),p(t),u(t))$, a.e on $[0, t_f]$,\n",
+ "\n",
+ "3. $\\displaystyle H(x(t),p(t),u(t)) = \\max_{w \\in U} H(x(t), p(t), w)$ a.e on $[0, t_f]$ (maximization condition),\n",
+ "\n",
+ "4. $\\displaystyle p(t_f) = J_c^T(x(t_f)) \\lambda = \\sum_{i=1}^k \\lambda_i \\nabla c_i(x(t_f))$ (transversality condition).\n",
+ "\n",
+ "</div>\n",
+ "\n",
+ "<div class=\"alert alert-info\">\n",
+ " \n",
+ "**_Assumptions_**\n",
+ " \n",
+ "We assume the following:\n",
+ " \n",
+ "* $U = \\mathrm{R}^m$,\n",
+ "* $\\forall (x,p) \\in \\mathrm{R}^n \\times \\mathrm{R}^n$, $u \\mapsto H(x,p,u)$ has a unique maximum denoted $\\varphi(x,p)$ (or $u[x,p]$ to recall the fact that it is the control law in feedback form),\n",
+ "* $\\varphi$ is smooth, that is at least $C^1$.\n",
+ " \n",
+ "</div>\n",
+ "\n",
+ "Under these assumptions, the maximization condition (3) is equivalent to the first order necessary condition of optimality and we have:\n",
+ "\n",
+ "$$\n",
+ " \\forall (x,p), \\quad \\nabla_u H(x,p, \\varphi(x,p)) = 0.\n",
+ "$$\n",
+ "\n",
+ "<!-- <video width=600 src=\"http://cots.perso.enseeiht.fr/indirect_simple_shooting/video2_PMP.mov\" controls>video2_PMP.mov</video>-->\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"640\"\n",
+ " height=\"360\"\n",
+ " src=\"https://www.youtube.com/embed/xedLNn08Kn4\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x1047b4310>"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.display import IFrame\n",
+ "IFrame(\"https://www.youtube.com/embed/xedLNn08Kn4\", width=640, height=360)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### c) The hidden true Hamiltonian\n",
+ "\n",
+ "Let us define the Hamiltonian \n",
+ "$$\n",
+ "h(z) := H(z, \\varphi(z)), \\quad z=(x,p).\n",
+ "$$\n",
+ "\n",
+ "This is a true Hamiltonian given by the maximization of the pseudo-Hamiltonian $H(z,u)$. By the chain rule, we have:\n",
+ "\n",
+ "$$\n",
+ " h'(z) = \\frac{\\partial H}{\\partial z}(z, \\varphi(z)) + \\frac{\\partial H}{\\partial u}(z, \\varphi(z)) \\cdot \\varphi'(z) = \\frac{\\partial H}{\\partial z}(z, \\varphi(z)),\n",
+ "$$\n",
+ "\n",
+ "since $\\frac{\\partial H}{\\partial u}(z, \\varphi(z))=0$. This leads to the remarkable fact that under our assumptions, equations (2) and (3) are equivalent to the Hamiltonian differential equation\n",
+ "\n",
+ "$$\n",
+ " \\dot{z}(t) = \\vec{h}(z(t)),\n",
+ "$$\n",
+ "\n",
+ "where $\\vec{h}(z) := (\\nabla_p h(z), -\\nabla_x h(z))$ is the **symplectic gradient** or **Hamiltonian system** associated to $h$.\n",
+ "\n",
+ "<!--<video width=600 src=\"http://cots.perso.enseeiht.fr/indirect_simple_shooting/video3_HAM.mov\" controls>video3_HAM.mov</video>-->\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"640\"\n",
+ " height=\"360\"\n",
+ " src=\"https://www.youtube.com/embed/inCRJZWT3Ng\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x1047b4b90>"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.display import IFrame\n",
+ "IFrame(\"https://www.youtube.com/embed/inCRJZWT3Ng\", width=640, height=360)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### d) Illustration of the resolution of the necessary conditions of optimality\n",
+ "<!--<video width=600 src=\"http://cots.perso.enseeiht.fr/indirect_simple_shooting/video3_ILL.mov\" controls>video3_ILL.mov</video>-->"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"640\"\n",
+ " height=\"360\"\n",
+ " src=\"https://www.youtube.com/embed/oRm8_Grs2Aw\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x1047b4710>"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.display import IFrame\n",
+ "IFrame(\"https://www.youtube.com/embed/oRm8_Grs2Aw\", width=640, height=360)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## II) Examples and boundary value problems\n",
+ "\n",
+ "### a) Simple 1D example\n",
+ "\n",
+ "**_Remark:_** The interest of this example is to present the methodology to solve the conditions given by the Pontryagin maximum principle.\n",
+ "\n",
+ "#### Step 1: Definition of the optimal control problem\n",
+ "\n",
+ "We consider the optimal control problem:\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\frac{1}{2} \\int_0^{t_f} u^2(t) \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = \\displaystyle -x(t)+u(t), \\quad u(t) \\in \\mathrm{R}, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = x_0 , \\quad x(t_f) = x_f,\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "with $t_f := 1$, $x_0 := -1$, $x_f := 0$ and $\\forall\\, t \\in[0, t_f]$, $x(t) \\in \\mathrm{R}$.\n",
+ "\n",
+ "#### Step 2: Application of the Pontryagin maximum principle\n",
+ "\n",
+ "The pseudo-Hamiltonian reads\n",
+ "\n",
+ "$$\n",
+ " H(x,p,u) := p \\, (-x+u) + p^0\\, \\frac{1}{2} u^2.\n",
+ "$$\n",
+ "\n",
+ "The PMP gives\n",
+ "\n",
+ "$$\n",
+ " \\left\\{ \n",
+ " \\begin{array}{rcl}\n",
+ " \\dot{x}(t) &=& \\phantom{-}\\nabla_p H[t] = -x(t)+u(t), \\\\[0.5em]\n",
+ " \\dot{p}(t) &=& -\\nabla_x H[t] = p(t), \\\\[0.5em]\n",
+ " 0 &=& \\phantom{-}\\nabla_u H[t] = p(t)+p^0 u(t),\n",
+ " \\end{array}\n",
+ " \\right.\n",
+ "$$\n",
+ "\n",
+ "where $[t] := (x(t),p(t),u(t))$. If $p^0 = 0$, then $p = 0$ by the third equation and so $(p, p^0) = (0,0)$ which is not. Hence, any *extremal* $(x, p, p^0, u)$ given by the PMP is said to be *normal*, that is $p^0 = -1$ (an extremal is said *abnormal* when $p^0=0$). \n",
+ "\n",
+ "**_Remark:_** We do not consider the transversality condition when the target $x_f$ is fixed. We can retrieve simply the Lagrange multiplier by the relation $p(t_f)=\\lambda$.\n",
+ "\n",
+ "**_Remark:_** The maximization condition,\n",
+ "$$\n",
+ "H[t] = \\max_{w \\in \\mathrm{R}} H(x(t), p(t), w),\n",
+ "$$\n",
+ "is equivalent here to the condition \n",
+ "$$\\nabla_u H[t] = 0$$ by concavity.\n",
+ "\n",
+ "Solving $\\nabla_u H[t] = 0$, the control satisfies $u(t) = u[x(t), p(t)] := p(t)$ where we have introduced the smooth function on $\\mathrm{R} \\times \\mathrm{R}$:\n",
+ "\n",
+ "$$\n",
+ "u[x,p] = p.\n",
+ "$$\n",
+ "\n",
+ "**_Remark:_** Plugging the control law in feedback form into the pseudo-Hamiltonian gives the (maximized) Hamiltonian:\n",
+ "\n",
+ "$$\n",
+ " h(z) = H(z, u[z]) = -px + \\frac{1}{2} p^2, \\quad z = (x, p).\n",
+ "$$\n",
+ "\n",
+ "#### Step 3: Transcription to a boundary value problem\n",
+ "\n",
+ "Now we have the control in feedback form, we introduce the following smooth *Two-Points Boundary Value Problem* (TPBVP or BVP for short):\n",
+ "\n",
+ "$$\n",
+ " \\left\\{ \n",
+ " \\begin{array}{rcl}\n",
+ " \\dot{x}(t) &=& -x(t)+u[x(t),p(t)] = -x(t) + p(t), \\\\[0.5em]\n",
+ " \\dot{p}(t) &=& p(t), \\\\[0.5em]\n",
+ " x(0) &=& x_0, \\quad x(t_f) = x_f.\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "The unknown of this BVP is the initial covector $p(0)$. Indeed, fixing $p_0:=p(0)$, then according to the [Cauchy-Lipschitz theorem](https://en.wikipedia.org/wiki/Picard–Lindelöf_theorem), there exists a unique maximal solution denoted \n",
+ "\n",
+ "$$\n",
+ "z(\\cdot, x_0, p_0) := (x(\\cdot, x_0, p_0), p(\\cdot, x_0, p_0))\n",
+ "$$\n",
+ "\n",
+ "satisfying the dynamics $\\dot{z}(t) = (-x(t)+p(t), p(t))$ together with the initial condition $z(0) = (x_0, p_0)$. \n",
+ "\n",
+ "<div class=\"alert alert-warning\">\n",
+ " \n",
+ "**_Goal_**\n",
+ " \n",
+ "The goal is thus to find the right initial covector $p_0$ such that $x(t_f, x_0, p_0) = x_f$.\n",
+ " \n",
+ "</div>\n",
+ "\n",
+ "#### Step 4: Solving the shooting equation\n",
+ "\n",
+ "From $\\dot{p}(t) = p(t)$, we get\n",
+ "$$\n",
+ "p(t, x_0, p_0) = e^t p_0,\n",
+ "$$\n",
+ "which leads to\n",
+ "$$\n",
+ "x(t, x_0, p_0) = p_0 \\sinh(t) + x_0 e^{-t}.\n",
+ "$$\n",
+ "Solving $x(t_f, x_0, p_0) = x_f$, we obtain\n",
+ "$$\n",
+ " p^*_0 = \\frac{x_f - x_0 e^{-t_f}}{\\sinh(t_f)} = \\frac{2}{e^{2}-1} \\approx 0.313.\n",
+ "$$\n",
+ "\n",
+ "**_Remark:_** To compute $p^*_0$, we have solved the linear *shooting equation* \n",
+ "\n",
+ "$$\n",
+ " S(p_0) := \\pi_x( z(t_f, x_0, p_0) ) - x_f = p_0 \\sinh(t_f) + x_0 e^{-t_f} - x_f,\n",
+ "$$\n",
+ "\n",
+ "with $\\pi_x(x,p) := x$. Solving $S(p_0) = 0$ is what we call the *indirect simple shooting method*.\n",
+ "\n",
+ "**_Remark:_** Note that thanks to the PMP, we have replaced the research of u (which is a function of time) by the research of an element of $\\mathrm{R}$: the covector $p_0$. The prize of such a drastic reduction is to work in the *cotangent space*, that is the trajectory $x$ is lifted in a bigger space and adjoined with a covector $p$: this makes the simple shooting method to be qualified of *indirect*. It is important to note that in the indirect methods we work with $z=(x,p)$ and not only with the trajectory $x$.\n",
+ "\n",
+ "<!--<video width=600 src=\"http://cots.perso.enseeiht.fr/indirect_simple_shooting/video4_EX1D.mov\" controls>video4_EX1D.mov</video>-->\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"640\"\n",
+ " height=\"360\"\n",
+ " src=\"https://www.youtube.com/embed/r4oYTkF76TA\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x1047b4ed0>"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.display import IFrame\n",
+ "IFrame(\"https://www.youtube.com/embed/r4oYTkF76TA\", width=640, height=360)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### b) Calculus of variations\n",
+ "\n",
+ "<!--<video width=600 src=\"http://cots.perso.enseeiht.fr/indirect_simple_shooting/video5_EXCV.mov\" controls>video5_EXCV.mov</video>-->\n",
+ "\n",
+ "**_Remark:_** The interest of this part is to present some particular cases in the context of calculus of variations for which our assumptions are satisfied."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"640\"\n",
+ " height=\"360\"\n",
+ " src=\"https://www.youtube.com/embed/Ud16jTQbsQ0\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x1047c2910>"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.display import IFrame\n",
+ "IFrame(\"https://www.youtube.com/embed/Ud16jTQbsQ0\", width=640, height=360)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### c) An energy min navigation problem \n",
+ "\n",
+ "**_Remark:_** The interest of this example is to present a case where we have some transversality conditions.\n",
+ "\n",
+ "We consider the optimal control problem:\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\frac{1}{2} \\int_0^{t_f} u_1^2(t) + u_2^2(t) \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = \\displaystyle (1, 0) + u(t), \\quad u(t) \\in \\mathrm{R}^2, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = (0, 0) , \\quad x_2(t_f) = 1.\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "The pseudo-Hamiltonian reads\n",
+ "\n",
+ "$$\n",
+ " H(x,p,u) := p_1 + (p | u) - \\frac{1}{2} (u_1^2+u_2^2), \\quad p^0 = -1.\n",
+ "$$\n",
+ "\n",
+ "The PMP gives:\n",
+ "\n",
+ "$$\n",
+ "\\dot{x} = (1,0) + u, \\quad \\dot{p} = 0, \\quad u = p, \\quad p(t_f) = (0, \\lambda),\n",
+ "$$\n",
+ "\n",
+ "and so we have to solve the BVP:\n",
+ "\n",
+ "$$\n",
+ " \\left\\{ \n",
+ " \\begin{array}{rcl}\n",
+ " \\dot{x}(t) &=& (1, 0) + p(t), \\\\[0.5em]\n",
+ " \\dot{p}(t) &=& 0, \\\\[0.5em]\n",
+ " x(0) &=& (0,0), \\quad x_2(t_f) = 1, \\quad p(t_f) = (0, \\lambda).\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "Computing we get,\n",
+ "\n",
+ "$$\n",
+ " u(t) = p(t) = (0, \\frac{1}{t_f}), \\quad \\lambda = \\frac{1}{t_f}, \\quad x(t) = (t, \\frac{t}{t_f}).\n",
+ "$$\n",
+ "\n",
+ "<!--<video width=600 src=\"http://cots.perso.enseeiht.fr/indirect_simple_shooting/video6_EXNAV.mov\" controls>video6_EXNAV.mov</video>-->\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## III) Indirect simple shooting\n",
+ "\n",
+ "### a) The shooting equation\n",
+ "\n",
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Boundary value problem_**\n",
+ " \n",
+ "Under our assumptions and thanks to the PMP we have to solve the following boundary value problem with a parameter $\\lambda$:\n",
+ "\n",
+ "$$\n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\dot{z}(t) = \\vec{H}(z(t),u[z(t)]), \\\\[0.5em]\n",
+ " x(0) = x_0, \\quad c(x(t_f)) = 0, \\quad p(t_f) = J_c^T(x(t_f)) \\lambda,\n",
+ " \\end{array}\n",
+ " \\right.\n",
+ "$$\n",
+ "\n",
+ "with $z=(x,p)$, with $u[z]$ the smooth control law in feedback form given by the maximization condition,\n",
+ "and where $\\vec{H}(z, u) := (\\nabla_p H(z,u), -\\nabla_x H(z,u))$.\n",
+ " \n",
+ "</div>\n",
+ "\n",
+ "**_Remark._** We can replace $\\dot{z}(t) = \\vec{H}(z(t),u[z(t)])$ by $\\dot{z}(t) = \\vec{h}(z(t))$,\n",
+ "where $h(z) = H(z, u[z])$ is the maximized Hamiltonian.\n",
+ "\n",
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Shooting function_**\n",
+ " \n",
+ "To solve the BVP, we define a set of nonlinear equations, the so-called the *shooting equations*. To do so, we introduce the *shooting function* $S \\colon \\mathrm{R}^n \\times \\mathrm{R}^k \\to \\mathrm{R}^k \\times \\mathrm{R}^n$:\n",
+ "\n",
+ "$$\n",
+ " S(p_0, \\lambda) := \n",
+ " \\begin{pmatrix}\n",
+ " c\\left( \\pi_x( z(t_f, x_0, p_0) ) \\right) \\\\\n",
+ " \\pi_p( z(t_f, x_0, p_0) ) - J_c^T \\left( \\pi_x( z(t_f, x_0, p_0) ) \\right) \\lambda\n",
+ " \\end{pmatrix}\n",
+ "$$\n",
+ "\n",
+ "where $\\pi_x(x,p) := x$ is the canonical projection into the state space, $\\pi_p(x,p) := p$ is the canonical projection into the co-state space, and where $z(t_f, x_0, p_0)$ is the solution at time $t_f$ of \n",
+ "$\\dot{z}(t) = \\vec{H}(z(t), u[z(t)]) = \\vec{h}(z(t))$, $z(0) = (x_0, p_0)$.\n",
+ " \n",
+ "</div>\n",
+ "\n",
+ "<div class=\"alert alert-warning\">\n",
+ " \n",
+ "**_Indirect simple shooting method_**\n",
+ " \n",
+ "Solving the BVP is equivalent to find a zero of the shooting function, that is to solve \n",
+ "\n",
+ "$$\n",
+ " S(p_0, \\lambda) = 0.\n",
+ "$$\n",
+ "\n",
+ "The *indirect simple shooting method* consists in solving this equation.\n",
+ "\n",
+ "</div>\n",
+ "\n",
+ "In order to solve the shooting equations, we need to compute the control law $u[\\cdot]$, the Hamiltonian system $\\vec{H}$ (or $\\vec{h}$), we need an [integrator method](https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations) to compute the *exponential map* $\\exp(t \\vec{H})$ defined by\n",
+ "$$\n",
+ "\\exp(t \\vec{H})(x_0, p_0) := z(t, x_0, p_0),\n",
+ "$$\n",
+ "and we need a [Newton-like](https://en.wikipedia.org/wiki/Newton%27s_method) solver to solve $S=0$.\n",
+ "\n",
+ "**_Remark:_** The notation with the exponential mapping is introduced because it is more explicit and permits to show that we need to define the Hamiltonian system and we need to compute the exponential, in order to compute an extremal solution of the PMP.\n",
+ "\n",
+ "**_Remark:_**\n",
+ "It is important to understand that if $(p_0^*, \\lambda^*)$ is solution of $S=0$, then the control $u(\\cdot) := u[z(\\cdot, x_0, p_0^*)]$ is a candidate as a solution of the optimal control problem. It is only a candidate and not a solution of the OCP since the PMP gives necessary conditions of optimality. We would have to go further to check whether the control is locally or globally optimal.\n"
+ ]
+ },
+ {
+ "attachments": {
+ "21f9cc6f-5061-4fbe-ab9b-b905c2389dc9.png": {
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"
+ }
+ },
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "<div align=\"center\">\n",
+ " <img src=\"attachment:21f9cc6f-5061-4fbe-ab9b-b905c2389dc9.png\" width=\"400\">\n",
+ "</div>\n",
+ "<div align=\"center\">\n",
+ "<i>\n",
+ "Figure: Illustration of the shooting method in the state-time space. The blue trajectory reaches the target in red. The shooting method consists in finding the right impulse to reach the target.\n",
+ "</i>\n",
+ "</div>"
+ ]
+ },
+ {
+ "attachments": {
+ "3760b746-f69d-4efb-b9e5-d92b43850334.png": {
+ "image/png": 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"
+ }
+ },
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div align=\"center\">\n",
+ " <img src=\"attachment:3760b746-f69d-4efb-b9e5-d92b43850334.png\" width=\"420\">\n",
+ "</div>\n",
+ "<div align=\"center\">\n",
+ "<i>\n",
+ "Figure: Illustration of the shooting method in the cotangent space. The blue extremal reaches the target in red.\n",
+ "</i>\n",
+ "</div>\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"640\"\n",
+ " height=\"360\"\n",
+ " src=\"https://www.youtube.com/embed/YVG2Z_TEkBQ\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x1047c6150>"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.display import IFrame\n",
+ "IFrame(\"https://www.youtube.com/embed/YVG2Z_TEkBQ\", width=640, height=360)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### b) The iteration of the Newton solver and the Jacobian of the shooting function\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"640\"\n",
+ " height=\"360\"\n",
+ " src=\"https://www.youtube.com/embed/hVbi9kShR90\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x1047c6a10>"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.display import IFrame\n",
+ "IFrame(\"https://www.youtube.com/embed/hVbi9kShR90\", width=640, height=360)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### c) A word on the Lagrange multiplier"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"640\"\n",
+ " height=\"360\"\n",
+ " src=\"https://www.youtube.com/embed/3VEi-UHAS6w\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x104745cd0>"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.display import IFrame\n",
+ "IFrame(\"https://www.youtube.com/embed/3VEi-UHAS6w\", width=640, height=360)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## IV) Numerical resolution of the shooting equations with the nutopy package"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# import nutopy and numpy packages\n",
+ "import nutopy as nt\n",
+ "import nutopy.tools as tools\n",
+ "import nutopy.ocp as ocp\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### a) Simple 1D example\n",
+ "\n",
+ "We recall the ocp:\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\frac{1}{2} \\int_0^{t_f} u^2(t) \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = \\displaystyle -x(t)+u(t), \\quad u(t) \\in \\mathrm{R}, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = x_0 , \\quad x(t_f) = x_f,\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "with $t_f := 1$, $x_0 := -1$, $x_f := 0$ and $\\forall\\, t \\in[0, t_f]$, $x(t) \\in \\mathrm{R}$.\n",
+ "\n",
+ "The (maximized) Hamiltonian is\n",
+ "\n",
+ "$$\n",
+ " h(z) = H(z, u[z]) = -px + \\frac{1}{2} p^2, \\quad z = (x, p).\n",
+ "$$\n",
+ "\n",
+ "and the Hamiltonian system is given by\n",
+ "\n",
+ "$$\n",
+ " \\dot{x} = -x+p, \\quad \\dot{p} = p.\n",
+ "$$\n",
+ "\n",
+ "The shooting function is\n",
+ "\n",
+ "$$\n",
+ " S(p_0) = \\pi_x(z(t_f, x_0, p_0)) - x_f.\n",
+ "$$\n",
+ "\n",
+ "The solution is $p_0^* \\approx 0.313$.\n",
+ "\n",
+ "#### Version 1: Using nutopy from the Hamiltonian system\n",
+ "\n",
+ "In this first version, we choose to solve the shooting equations following the steps described in Section III)-a). In the next version, we will use the nutopy package in a more natural way.\n",
+ "\n",
+ "We need the following methods: \n",
+ "[nutopy.ivp.exp](https://ct.gitlabpages.inria.fr/nutopy/api/ivp/ivp-exp.html),\n",
+ "[nutopy.nle.solve](https://ct.gitlabpages.inria.fr/nutopy/api/nle/nle-solve.html).\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 8.073217526767197e-01 1.000000000000000e+00\n",
+ " 2 1.428248003892962e-08 3.130352977215060e-01\n",
+ " 3 6.938893903907228e-18 3.130352855682848e-01\n",
+ " 4 6.938893903907228e-18 3.130352855682848e-01\n",
+ " 5 1.428248013607414e-08 3.130352734150637e-01\n",
+ " 6 6.938893903907228e-18 3.130352855682848e-01\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = 0.3130352855682848\n",
+ " f(xsol) = -6.938893903907228e-18\n",
+ " nfev = 6\n",
+ " njev = 2\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ "NLE outputs: \n",
+ "\n",
+ " p0_sol = 0.3130352855682848 \n",
+ " shoot = -6.938893903907228e-18 \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Definition of the Hamiltonian system\n",
+ "def hv(x, p):\n",
+ " return np.array([-x + p, p])\n",
+ "\n",
+ "# Definition of the exponential mapping\n",
+ "# The exp function computes the exponential of a system given in the first argument of the function\n",
+ "# The system has to be given in the form: f(t, z)\n",
+ "def exponential(t, hvfun, x0, p0):\n",
+ " sol = nt.ivp.exp( lambda t, z: hvfun(z[0], z[1]), # we work with z=(x,p): f(t, z) = hvfun(x, p)\n",
+ " t, # final time\n",
+ " 0.0, # initial time\n",
+ " np.array([x0, p0]) ) # z0 = (x0, p0)\n",
+ " return sol.xf[0], sol.xf[1] # return z(t) = (x(t), p(t))\n",
+ "\n",
+ "# Definition of the shooting equation\n",
+ "def shoot(p0):\n",
+ " tf = 1.0\n",
+ " x0 = -1.0\n",
+ " xf_target = 0.0\n",
+ " xf, pf = exponential(tf, hv, x0, p0)\n",
+ " return xf - xf_target # x(tf, x0, p0) - xf_target\n",
+ "\n",
+ "# The shooting method: resolution of the shooting equation\n",
+ "p0_guess = 1.0 # initial guess for the Newton solver\n",
+ "sol = nt.nle.solve(shoot, p0_guess); # call to the Newton solver\n",
+ "p0_sol = sol.x\n",
+ "\n",
+ "print('NLE outputs: ', '\\n\\n p0_sol =', p0_sol, '\\n shoot =', shoot(p0_sol), '\\n')\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Version 2: Using nutopy from the Hamiltonian\n",
+ "\n",
+ "In this version we use nutopy in a more natural way. See this [page](https://ct.gitlabpages.inria.fr/gallery/smooth_case/smooth_case_full.html) for a more detailed example of the use of nutopy.\n",
+ "\n",
+ "We need the following methods:\n",
+ "[nutopy.ocp](https://ct.gitlabpages.inria.fr/nutopy/api/ocp.html),\n",
+ "[nutopy.nle.solve](https://ct.gitlabpages.inria.fr/nutopy/api/nle/nle-solve.html).\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 8.073217526767197e-01 1.000000000000000e+00\n",
+ " 2 1.428248003892962e-08 3.130352977215060e-01\n",
+ " 3 6.938893903907228e-18 3.130352855682848e-01\n",
+ " 4 6.938893903907228e-18 3.130352855682848e-01\n",
+ " 5 1.428248013607414e-08 3.130352734150637e-01\n",
+ " 6 6.938893903907228e-18 3.130352855682848e-01\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [0.31303529]\n",
+ " f(xsol) = [-6.9388939e-18]\n",
+ " nfev = 6\n",
+ " njev = 2\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ "NLE\t: \n",
+ "\n",
+ " p0_sol = [0.31303529] \n",
+ " shoot = [-6.9388939e-18] \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Definition of the maximized Hamiltonian and its derivatives\n",
+ "# The derivatives may be computed by hand as here or by Automatic Differentiation for instance\n",
+ "\n",
+ "def dhfun(t, x, dx, p, dp):\n",
+ " # dh = dh_x dx + dh_p dp\n",
+ " hd = -p*dx + (-x+p)*dp\n",
+ " return hd\n",
+ " \n",
+ "def d2hfun(t, x, dx, d2x, p, dp, d2p):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ " hdd = -d2p*dx + (-d2x+d2p)*dp\n",
+ " return hdd\n",
+ "\n",
+ "@tools.tensorize(dhfun, d2hfun, tvars=(2, 3))\n",
+ "def hfun(t, x, p):\n",
+ " h = p * (-x + p) - 0.5*p**2\n",
+ " return h\n",
+ "\n",
+ "h = ocp.Hamiltonian(hfun) # The Hamiltonian object\n",
+ "\n",
+ "f = ocp.Flow(h) # The flow associated to the Hamiltonian object is \n",
+ " # the exponential mapping with its derivative\n",
+ " # that can be used to define the Jacobian of the \n",
+ " # shooting function\n",
+ "\n",
+ "# Definition of the shooting function\n",
+ "def shoot(p0):\n",
+ " t0 = 0.0\n",
+ " tf = 1.0\n",
+ " x0 = np.array([-1.0])\n",
+ " xf_target = np.array([ 0.0])\n",
+ " xf, pf = f(t0, x0, p0, tf) # We use the flow to get z(tf, x0, p0)\n",
+ " s = xf - xf_target # x(tf, x0, p0) - xf_target\n",
+ " return s\n",
+ "\n",
+ "# The shooting method: resolution of the shooting equation\n",
+ "p0_guess = np.array([1.0])\n",
+ "sol = nt.nle.solve(shoot, p0_guess);\n",
+ "p0_sol = sol.x\n",
+ "\n",
+ "print('NLE\\t: ', '\\n\\n p0_sol =', p0_sol, '\\n shoot =', shoot(p0_sol), '\\n') "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 8.073217526767197e-01 1.000000000000000e+00\n",
+ " 2 3.184008612322486e-11 3.130352855411916e-01\n",
+ " 3 1.110223024625157e-16 3.130352855682850e-01\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [0.31303529]\n",
+ " f(xsol) = [1.11022302e-16]\n",
+ " nfev = 3\n",
+ " njev = 1\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ "NLE\t: \n",
+ "\n",
+ " p0_sol = [0.31303529] \n",
+ " shoot = [1.11022302e-16] \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# We define the derivative of the shooting function and use it for the resolution of S=0. \n",
+ "# Previously, the Jacobian was computed by finite differences.\n",
+ "# We do not provide S'(p0) but S'(p0).dp0. \n",
+ "# In our scalar case, it is quite similar but in general, it simpler to provide S'(p0).dp0.\n",
+ "\n",
+ "def dshoot(p0, dp0):\n",
+ " t0 = 0.0\n",
+ " tf = 1.0\n",
+ " x0 = np.array([-1.0])\n",
+ " (xf, dxf), _ = f(t0, x0, (p0, dp0), tf)\n",
+ " ds = dxf\n",
+ " return ds\n",
+ "\n",
+ "shoot = nt.tools.tensorize(dshoot)(shoot) # the use of tensorize permits to code S'(p0).dp0 instead of S'(p0)\n",
+ "\n",
+ "# The shooting method: resolution of the shooting equation\n",
+ "p0_guess = np.array([1.0])\n",
+ "sol = nt.nle.solve(shoot, p0_guess, df=shoot);\n",
+ "p0_sol = sol.x\n",
+ "\n",
+ "print('NLE\\t: ', '\\n\\n p0_sol =', p0_sol, '\\n shoot =', shoot(p0_sol), '\\n') "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### b) Calculus of variations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**_Problem 1:_**\n",
+ "\n",
+ "Les us consider the following problem which consists in computing the Euclidean distance between two points of the plan:\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\frac{1}{2} \\int_0^{t_f} ||u(t)||^2 \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = \\displaystyle u(t), \\quad u(t) \\in \\mathrm{R}^2, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = A , \\quad x(t_f) = B,\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "with $t_f > 0$ fixed and $A, B \\in \\mathrm{R}^2$ given.\n",
+ "\n",
+ "The (maximized) Hamiltonian is\n",
+ "\n",
+ "$$\n",
+ " h(z) = H(z, u[z]) = \\frac{1}{2} ||p||^2, \\quad z = (x, p).\n",
+ "$$\n",
+ "\n",
+ "and the Hamiltonian system is given by\n",
+ "\n",
+ "$$\n",
+ " \\dot{x} = p, \\quad \\dot{p} = 0.\n",
+ "$$\n",
+ "\n",
+ "The shooting function is\n",
+ "\n",
+ "$$\n",
+ " S(p_0) = \\pi_x(z(t_f, A, p_0)) - B.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 1.272792206135785e+00 1.414213562373095e-01\n",
+ " 2 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 3 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 4 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 5 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 6 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 7 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 8 7.954951288348694e-02 1.493763075256582e+00\n",
+ " 9 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 10 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 11 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 12 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 13 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 14 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 15 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 16 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 17 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 18 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 19 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 20 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 21 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 22 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 23 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 24 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 25 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 26 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 27 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 28 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 29 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 30 3.140184917367550e-16 1.414213562373095e+00\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [1. 1.]\n",
+ " f(xsol) = [2.22044605e-16 2.22044605e-16]\n",
+ " nfev = 30\n",
+ " njev = 2\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ "NLE\t: \n",
+ "\n",
+ " p0_sol = [1. 1.] \n",
+ " shoot = [2.22044605e-16 2.22044605e-16] \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Definition of the maximized Hamiltonian and its derivatives\n",
+ "\n",
+ "def dhfun(t, x, dx, p, dp):\n",
+ " # dh = dh_x dx + dh_p dp\n",
+ " hd = np.dot(p, dp)\n",
+ " return hd\n",
+ " \n",
+ "def d2hfun(t, x, dx, d2x, p, dp, d2p):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ " hdd = np.dot(d2p, dp)\n",
+ " return hdd\n",
+ "\n",
+ "@tools.tensorize(dhfun, d2hfun, tvars=(2, 3))\n",
+ "def hfun(t, x, p):\n",
+ " h = 0.5*np.dot(p, p)\n",
+ " return h\n",
+ "\n",
+ "h = ocp.Hamiltonian(hfun) # The Hamiltonian object\n",
+ "\n",
+ "f = ocp.Flow(h) # The flow associated to the Hamiltonian object is \n",
+ " # the exponential mapping with its derivative\n",
+ " # that can be used to define the Jacobian of the \n",
+ " # shooting function\n",
+ "\n",
+ "# Definition of the shooting function and its derivative\n",
+ "# the use of tensorize permits to code S'(p0).dp0 instead of S'(p0)\n",
+ "def dshoot(p0, dp0):\n",
+ " t0 = 0.0\n",
+ " tf = 1.0\n",
+ " A = np.array([ 0.0, 0.0])\n",
+ " (xf, dxf), _ = f(t0, A, (p0, dp0), tf)\n",
+ " ds = dxf\n",
+ " return ds\n",
+ "\n",
+ "@tools.tensorize(dshoot)\n",
+ "def shoot(p0):\n",
+ " t0 = 0.0\n",
+ " tf = 1.0\n",
+ " A = np.array([ 0.0, 0.0])\n",
+ " B = np.array([ 1.0, 1.0])\n",
+ " xf, pf = f(t0, A, p0, tf) # We use the flow to get z(tf, x0, p0)\n",
+ " s = xf - B # x(tf, x0, p0) - B\n",
+ " return s\n",
+ "\n",
+ "# The shooting method: resolution of the shooting equation\n",
+ "p0_guess = np.array([0.1, 0.1])\n",
+ "sol = nt.nle.solve(shoot, p0_guess, df=shoot);\n",
+ "p0_sol = sol.x\n",
+ "\n",
+ "print('NLE\\t: ', '\\n\\n p0_sol =', p0_sol, '\\n shoot =', shoot(p0_sol), '\\n') "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**_Problem 2:_**\n",
+ "\n",
+ "Les us consider the following problem which consists in computing the Euclidean distance between a point and a line of the plan:\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\frac{1}{2} \\int_0^{t_f} ||u(t)||^2 \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = \\displaystyle u(t), \\quad u(t) \\in \\mathrm{R}^2, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = A , \\quad x_1(t_f) = 1,\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "with $t_f > 0$ fixed and $A\\in \\mathrm{R}^2$ given.\n",
+ "\n",
+ "The (maximized) Hamiltonian and the Hamiltonian system are similar to Problem 1. We have the transversality condition\n",
+ "\n",
+ "$$\n",
+ " p(t_f) = (\\lambda, 0).\n",
+ "$$\n",
+ "\n",
+ "In this case, the shooting function is given by\n",
+ "\n",
+ "$$\n",
+ " S(p_0, \\lambda) = \\left( (x_1(t_f, A, p_0) - 1, p_1(t_f, A, p_0) - \\lambda, p_2(t_f, A, p_0) \\right).\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 9.899494936611666e-01 5.196152422706632e-01\n",
+ " 2 5.265754007445733e+01 5.341221252310977e+01\n",
+ " 3 2.215058419779381e-02 1.398638437904777e+00\n",
+ " 4 1.337306002566763e-04 1.414308127348630e+00\n",
+ " 5 2.220446049250333e-16 1.414213562373095e+00\n",
+ " 6 2.220446049250313e-16 1.414213562373095e+00\n",
+ " 7 2.220446049250313e-16 1.414213562373095e+00\n",
+ " 8 6.686530012833813e-05 1.414260844070578e+00\n",
+ " 9 2.220446049250313e-16 1.414213562373095e+00\n",
+ " 10 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 11 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 12 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 13 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 14 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 15 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 16 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 17 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 18 3.140184917367550e-16 1.414213562373095e+00\n",
+ " 19 3.140184917367550e-16 1.414213562373095e+00\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [ 1.00000000e+00 -2.97001333e-23 1.00000000e+00]\n",
+ " f(xsol) = [-2.22044605e-16 0.00000000e+00 -2.97001333e-23]\n",
+ " nfev = 19\n",
+ " njev = 2\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ "NLE\t: \n",
+ "\n",
+ " p0_sol = [ 1.00000000e+00 -2.97001333e-23] \n",
+ " lambda = 1.0 \n",
+ " \n",
+ " shoot = [-2.22044605e-16 0.00000000e+00 -2.97001333e-23] \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Definition of the maximized Hamiltonian and its derivatives\n",
+ "\n",
+ "def dhfun(t, x, dx, p, dp):\n",
+ " # dh = dh_x dx + dh_p dp\n",
+ " hd = np.dot(p, dp)\n",
+ " return hd\n",
+ " \n",
+ "def d2hfun(t, x, dx, d2x, p, dp, d2p):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ " hdd = np.dot(d2p, dp)\n",
+ " return hdd\n",
+ "\n",
+ "@tools.tensorize(dhfun, d2hfun, tvars=(2, 3))\n",
+ "def hfun(t, x, p):\n",
+ " h = 0.5*(p[0]**2+p[1]**2)\n",
+ " return h\n",
+ "\n",
+ "h = ocp.Hamiltonian(hfun) # The Hamiltonian object\n",
+ "\n",
+ "f = ocp.Flow(h) # The flow associated to the Hamiltonian object is \n",
+ " # the exponential mapping with its derivative\n",
+ " # that can be used to define the Jacobian of the \n",
+ " # shooting function\n",
+ "\n",
+ "# Definition of the shooting function and its derivative\n",
+ "# the use of tensorize permits to code S'(p0).dp0 instead of S'(p0)\n",
+ "def dshoot(y, dy):\n",
+ " p0 = y[0:2]\n",
+ " l = y[2]\n",
+ " dp0 = dy[0:2]\n",
+ " dl = dy[2]\n",
+ " t0 = 0.0\n",
+ " tf = 1.0\n",
+ " A = np.array([ 0.0, 0.0])\n",
+ " (xf, dxf), (pf, dpf) = f(t0, A, (p0, dp0), tf)\n",
+ " ds = np.zeros([3])\n",
+ " ds[0] = dxf[0]\n",
+ " ds[1] = dpf[0]\n",
+ " ds[2] = dpf[1]\n",
+ " return ds\n",
+ "\n",
+ "@tools.tensorize(dshoot)\n",
+ "def shoot(y):\n",
+ " p0 = y[0:2]\n",
+ " l = y[2]\n",
+ " t0 = 0.0\n",
+ " tf = 1.0\n",
+ " A = np.array([ 0.0, 0.0])\n",
+ " xf, pf = f(t0, A, p0, tf)\n",
+ " s = np.zeros([3])\n",
+ " s[0] = xf[0] - 1.0\n",
+ " s[1] = pf[0] - l\n",
+ " s[2] = pf[1]\n",
+ " return s\n",
+ "\n",
+ "# The shooting method: resolution of the shooting equation\n",
+ "y_guess = np.array([0.1, 0.1, 0.5])\n",
+ "sol = nt.nle.solve(shoot, y_guess, df=shoot);\n",
+ "y_sol = sol.x\n",
+ "\n",
+ "print('NLE\\t: ', '\\n\\n p0_sol =', y_sol[0:2], '\\n lambda =', y_sol[2], '\\n', '\\n shoot =', shoot(y_sol), '\\n') "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### c) An energy min navigation problem - exercice"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Les us consider the following problem in the plan:\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\frac{1}{2} \\int_0^{t_f} ||u(t)||^2 \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = \\displaystyle (1, 0) + u(t), \\quad u(t) \\in \\mathrm{R}^2, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = A , \\quad x_2(t_f) = 1,\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "with $t_f = 1$ fixed and $A = (0,0) \\in \\mathrm{R}^2$ given.\n",
+ "\n",
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 1:_**\n",
+ " \n",
+ "Write the maximized Hamiltonian, the Hamiltonian system and the transversality condition given by the PMP.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Answer 1:** To complete here (double-click on the line to complete)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 2:_**\n",
+ " \n",
+ "Write the shooting function $S(p_0, \\lambda)$, $p_0 \\in \\mathrm{R}^2$, $\\lambda \\in \\mathrm{R}$.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Answer 2:** To complete here (double-click on the line to complete)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 3:_**\n",
+ " \n",
+ "Complete/Modify the following code to find the solution of the shooting equations.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 0.000000000000000e+00 5.196152422706632e-01\n",
+ " 2 0.000000000000000e+00 5.196152422706632e-01\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [0.1 0.1 0.5]\n",
+ " f(xsol) = [0. 0. 0.]\n",
+ " nfev = 2\n",
+ " njev = 1\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ "NLE\t: \n",
+ "\n",
+ " p0_sol = [0.1 0.1] \n",
+ " lambda = 0.5 \n",
+ " \n",
+ " shoot = [0. 0. 0.] \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Definition of the maximized Hamiltonian and its derivatives\n",
+ "\n",
+ "def dhfun(t, x, dx, p, dp):\n",
+ " # dh = dh_x dx + dh_p dp\n",
+ " hd = 0.0 ### TO COMPLETE\n",
+ " return hd\n",
+ " \n",
+ "def d2hfun(t, x, dx, d2x, p, dp, d2p):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ " hdd = 0.0 ### TO COMPLETE\n",
+ " return hdd\n",
+ "\n",
+ "@tools.tensorize(dhfun, d2hfun, tvars=(2, 3))\n",
+ "def hfun(t, x, p):\n",
+ " h = 0.0 ### TO COMPLETE\n",
+ " return h\n",
+ "\n",
+ "h = ocp.Hamiltonian(hfun) # The Hamiltonian object\n",
+ "\n",
+ "f = ocp.Flow(h) # The flow associated to the Hamiltonian object is \n",
+ " # the exponential mapping with its derivative\n",
+ " # that can be used to define the Jacobian of the \n",
+ " # shooting function\n",
+ "\n",
+ "# Definition of the shooting function and its derivative\n",
+ "# the use of tensorize permits to code S'(p0).dp0 instead of S'(p0)\n",
+ "def dshoot(y, dy): ### TO COMPLETE\n",
+ " ds = np.zeros([3])\n",
+ " return ds\n",
+ "\n",
+ "@tools.tensorize(dshoot) ### TO COMPLETE\n",
+ "def shoot(y):\n",
+ " s = np.zeros([3])\n",
+ " return s\n",
+ "\n",
+ "# The shooting method: resolution of the shooting equation\n",
+ "y_guess = np.array([0.1, 0.1, 0.5])\n",
+ "sol = nt.nle.solve(shoot, y_guess, df=shoot);\n",
+ "y_sol = sol.x\n",
+ "\n",
+ "print('NLE\\t: ', '\\n\\n p0_sol =', y_sol[0:2], '\\n lambda =', y_sol[2], '\\n', '\\n shoot =', shoot(y_sol), '\\n') "
+ ]
+ }
+ ],
+ "metadata": {
+ "celltoolbar": "Tags",
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/doc/exercices/bsb_turnpike_regularized.ipynb b/doc/exercices/bsb_turnpike_regularized.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..59ff7b76123787c611cb8717818872d51340358a
--- /dev/null
+++ b/doc/exercices/bsb_turnpike_regularized.ipynb
@@ -0,0 +1,1045 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solving the 1D integrator by indirect multiple shooting: the Bang-Singular-Bang case on a turnpike problem "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Author: Olivier Cots\n",
+ "* Date: March 2021\n",
+ "\n",
+ "------"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## I) Description of the optimal control problem"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We consider the following optimal control problem:\n",
+ "\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\int_0^{t_f} x^2(t) \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = f(x(t), u(t)) := \\displaystyle u(t), \\quad |u(t)| \\le 1, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = 1, \\quad x(t_f) = 1/2.\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "To this optimal control problem is associated the stationnary optimization problem\n",
+ "\n",
+ "$$\n",
+ " \\min_{(x, u)} \\{~ x^2 ~ | ~ (x, u) \\in \\mathrm{R} \\times [-1, 1],~ f(x,u) = u = 0\\}.\n",
+ "$$\n",
+ "\n",
+ "The static solution is thus $(x^*, u^*) = (0, 0)$. This solution may be seen as the static pair $(x, u)$ which minimizes the cost $J(u)$ under\n",
+ "the constraint $u \\in [-1, 1]$.\n",
+ "It is well known that this problem is what we call a *turnpike* optimal control problem.\n",
+ "Hence, if the final time $t_f$ is long enough the solution is of the following form: \n",
+ "starting from $x(0)=1$, reach as fast as possible the static solution, stay at the static solution as long as possible before reaching\n",
+ "the target $x(t_f)=1/2$. In this case, the optimal control would be\n",
+ "\n",
+ "$$\n",
+ " u(t) = \\left\\{ \n",
+ " \\begin{array}{lll}\n",
+ " -1 & \\text{if} & t \\in [0, t_1], \\\\[0.5em]\n",
+ " \\phantom{-}0 & \\text{if} & t \\in (t_1, t_2], \\\\[0.5em]\n",
+ " +1 & \\text{if} & t \\in (t_2, t_f],\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "with $0 < t_1 < t_2 < t_f$. We say that the control is *Bang-Singular-Bang*. A Bang arc corresponds to $u \\in \\{-1, 1\\}$ while a singular control corresponds to $u \\in (-1, 1)$. Since the optimal control law is discontinuous, then to solve this optimal control problem by indirect methods and find the *switching times* $t_1$ and $t_2$, we need to implement what we call a *multiple shooting method*. In the next section we introduce a regularization technique to force the control to be in the set $(-1,1)$ and to be smooth. In this context, we will be able to implement a simple shooting method and determine the structure of the optimal control law. Thanks to the simple shooting method, we will have the structure of the optimal control law together with an approximation of the switching times that we will use as initial guess for the multiple shooting method that we present in the last section.\n",
+ "\n",
+ "**_Remark 1._** See this [page](https://ct.gitlabpages.inria.fr/gallery/shooting_tutorials/simple_shooting_general.html) for a general presentation of the simple shooting method.\n",
+ "\n",
+ "**_Remark 2._** In this particular example, the singular control does not depend on the costate $p$ since it is constant. This happens in low dimension. This could be taken into consideration to simplify the definition of the multiple shooting method. However, to stay general, we will not consider this particular property in this notebook. \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## II) Regularization and simple shooting"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We make the following regularization:\n",
+ "\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\int_0^{t_f} (x^2(t) - \\varepsilon\\ln(1-u^2(t))) \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = f(x(t), u(t)) := \\displaystyle u(t), \\quad |u(t)| \\le 1, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = 1, \\quad x(t_f) = 1/2.\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "Our goal is to determine the structure of the optimal control problem when $(\\varepsilon, t_f) = (0, 2)$. The problem is simpler to solver when $\\varepsilon$ is bigger and $t_f$ is smaller. It is also smooth whenever $\\varepsilon>0$. Hence, we will start by solving the problem for $(\\varepsilon, t_f) = (1, 1)$. In a second step, we will decrease the *penalization term* $\\varepsilon$ and in a final step, we will increase the final time $t_f$ to the final value $2$.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Preliminaries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# import packages\n",
+ "import nutopy as nt\n",
+ "import nutopy.tools as tools\n",
+ "import nutopy.ocp as ocp\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "#plt.rcParams['figure.figsize'] = [10, 5]\n",
+ "plt.rcParams['figure.dpi'] = 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Finite differences function for scalar functionnal\n",
+ "# Return f'(x).dx\n",
+ "def finite_diff(fun, x, dx, *args, **kwargs):\n",
+ " v_eps = np.finfo(float).eps\n",
+ " t = np.sqrt(v_eps) * np.sqrt(np.maximum(1.0, np.abs(x))) / np.sqrt(np.maximum(1.0, np.abs(dx)))\n",
+ " j = (fun(x + t*dx, *args, **kwargs) - fun(x, *args, **kwargs)) / t\n",
+ " return j"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Parameters\n",
+ "\n",
+ "t0 = 0.0\n",
+ "x0 = np.array([1.0])\n",
+ "xf_target = np.array([0.5])\n",
+ "\n",
+ "e_init = 1.0\n",
+ "e_final = 0.002 #\n",
+ "\n",
+ "tf_init = 1.0 # With this value the problem is simpler to solver since the trajectory stay \n",
+ " # less time around the static solution\n",
+ "tf_final = 2.0"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Maximized Hamiltonian and its derivatives"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The pseudo-Hamiltonian is (in the normal case)\n",
+ "\n",
+ "$$\n",
+ " H(x,p,u,\\varepsilon) = pu - x^2 + \\varepsilon ln(1-u^2).\n",
+ "$$\n",
+ "\n",
+ "Note that we put the parameter $\\varepsilon$ into the arguments of the pseudo-Hamiltonian since we will vary it."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 1:_**\n",
+ " \n",
+ "Give the maximizing control $u[p, \\varepsilon]$, that is the control in feedback form solution of the maximization condition.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Answer 1:** To complete here (double-click on the line to complete)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 2:_**\n",
+ " \n",
+ "Complete the code of the maximizing control and its derivative with respect to $p$.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Control in feedback form\n",
+ "@tools.vectorize(vvars=(1,))\n",
+ "def ufun(p, e):\n",
+ "# u = 0 ### TO COMPLETE\n",
+ " u = (-e + np.sqrt(e**2+p**2))/p \n",
+ " return u\n",
+ "\n",
+ "def dufun(p, e):\n",
+ "# du = 0 ### TO COMPLETE\n",
+ " s = np.sqrt(e**2+p**2)\n",
+ " du = 1.0/s + (e - s)/p**2\n",
+ " return du"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Definition of the maximized Hamiltonian and its derivatives\n",
+ "# The second derivative d2hfun is computed by finite differences for a part\n",
+ "def dhfun(t, x, dx, p, dp, e):\n",
+ " # dh = dh_x dx + dh_p dp\n",
+ " u = ufun(p, e)\n",
+ " du = dufun(p, e)\n",
+ " hd = (u+p*du+2.0*e*u*du/(u**2-1.0))*dp - 2.0*x*dx\n",
+ " return hd\n",
+ "\n",
+ "def d2hfun(t, x, dx, d2x, p, dp, d2p, e):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ " d2h_xx = -2.0*dx*d2x # dh_xx dx d2x\n",
+ " dh_p = lambda p: dhfun(t, x, 0.0, p, dp, e) # dh_px = 0 so we can put dx = 0\n",
+ " d2h_pp = finite_diff(dh_p, p, d2p) # dh_pp dp d2p\n",
+ " hdd = d2h_xx + d2h_pp\n",
+ " return hdd\n",
+ "\n",
+ "@tools.tensorize(dhfun, d2hfun, tvars=(2, 3))\n",
+ "def hfun(t, x, p, e):\n",
+ " u = ufun(p, e)\n",
+ " h = p*u - x**2 + e*(np.log(1.0-u**2))\n",
+ " return h\n",
+ "\n",
+ "h = ocp.Hamiltonian(hfun) # The Hamiltonian object\n",
+ "\n",
+ "f = ocp.Flow(h) # The flow associated to the Hamiltonian object is \n",
+ " # the exponential mapping with its derivative\n",
+ " # that can be used to define the Jacobian of the \n",
+ " # shooting function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Shooting function and its derivative"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The shooting function is\n",
+ "\n",
+ "$$\n",
+ " S(p_0, \\varepsilon, t_f) = \\pi_x(z(t_f, 1, p_0, \\varepsilon)) - 1/2,\n",
+ "$$\n",
+ "\n",
+ "where $z(t_f, x_0, p_0, \\varepsilon)$ is the solution of the associated Hamiltonian system \n",
+ "(see [here](https://ct.gitlabpages.inria.fr/gallery/simple_shooting_general/simple_shooting_general.html) for details)\n",
+ "with the initial condition $z(0) = (x_0, p_0)$. Note that the Hamiltonian system depends on $\\varepsilon$. We put $\\varepsilon$ and $t_f$ into \n",
+ "the arguments of the shooting function since we will vary them.\n",
+ "\n",
+ "<div class=\"alert alert-warning\">\n",
+ "\n",
+ "**Procedure**\n",
+ "\n",
+ "First solve $S=0$ for $(\\varepsilon, t_f) = (1,1)$ then decrease $\\varepsilon$ to $0.01$, and finish by increasing $t_f$ to 2.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 3:_**\n",
+ " \n",
+ "Complete the code of the shooting function and its derivative with respect to $p_0$ against the vector $dp_0$.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Definition of the shooting function\n",
+ "def dshoot(p0, dp0, e, tf):\n",
+ "# s = 0 ### TO COMPLETE\n",
+ "# ds = 0 ### TO COMPLETE\n",
+ " (xf, dxf), _ = f(t0, x0, (p0, dp0), tf, e)\n",
+ " s = xf - xf_target # code duplication (in order to compute dxf, shooting also needs \n",
+ " # to compute xf; accordingly, full=True)\n",
+ " ds = dxf\n",
+ " return s, ds\n",
+ "\n",
+ "@tools.tensorize(dshoot, tvars=(1,), full=True)\n",
+ "def shoot(p0, e, tf):\n",
+ "# s = 0 ### TO COMPLETE: use the flow f, the parameters t0, x0 and xf_target\n",
+ " xf, pf = f(t0, x0, p0, tf, e) # We use the flow to get z(tf, x0, p0)\n",
+ " s = xf - xf_target # x(tf, x0, p0) - xf_target\n",
+ " return s"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Function to plot the solution\n",
+ "def plotSolution(p0, e, tf):\n",
+ "\n",
+ " N = 200\n",
+ " tspan = list(np.linspace(t0, tf, N+1))\n",
+ " xf, pf = f(t0, x0, p0, tspan, e)\n",
+ " u = ufun(pf, e)\n",
+ "\n",
+ " fig = plt.figure()\n",
+ " ax = fig.add_subplot(511); ax.plot(tspan, xf); ax.set_xlabel('t'); ax.set_ylabel('$x$'); ax.axhline(0, color='k')\n",
+ " ax = fig.add_subplot(513); ax.plot(tspan, pf); ax.set_xlabel('t'); ax.set_ylabel('$p$'); ax.axhline(0, color='k')\n",
+ " ax = fig.add_subplot(515); ax.plot(tspan, u); ax.set_xlabel('t'); ax.set_ylabel('$u$'); ax.axhline(0, color='k')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Resolution of the regularized problem"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 9.225527956247914e-01 1.000000000000000e-01\n",
+ " 2 1.328510039876105e-01 2.933843238918098e+00\n",
+ " 3 7.295873671084141e-02 2.551952326284172e+00\n",
+ " 4 3.048709252432280e-02 2.086745717585143e+00\n",
+ " 5 4.420525056492819e-03 2.223849330434452e+00\n",
+ " 6 2.283580968987509e-04 2.206487218725369e+00\n",
+ " 7 1.831090794324197e-06 2.205541459926580e+00\n",
+ " 8 7.509122212923103e-10 2.205548983174077e+00\n",
+ " 9 2.775557561562891e-15 2.205548980090132e+00\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [-2.20554898]\n",
+ " f(xsol) = [-2.77555756e-15]\n",
+ " nfev = 9\n",
+ " njev = 1\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Shooting for (tf, e) = (tf_init, e_init)\n",
+ "p0_guess = np.array([0.1])\n",
+ "nlefun = lambda p0: shoot(p0, e_init, tf_init)\n",
+ "sol_nle = nt.nle.solve(nlefun, p0_guess, df=nlefun)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 3 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot solution for (tf, e) = (tf_init, e_init)\n",
+ "plotSolution(sol_nle.x, e_init, tf_init)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Definition of the homotopic function and its first order derivative\n",
+ "# This function is used to solve S=0 for different values of e=epsilon and tf.\n",
+ "def dhomfun(p0, dp0, e, de, tf, dtf):\n",
+ " #\n",
+ " (xf, dxf), (pf, dpf) = f(t0, x0, (p0, dp0), tf, e) \n",
+ " #\n",
+ " s = xf - xf_target\n",
+ " #\n",
+ " ds_p0 = dxf\n",
+ " ds_tf = ufun(pf, e) * dtf # dS_tf dtf = u dtf\n",
+ " #\n",
+ " fun = lambda e: float(f(t0, x0, p0, tf, e)[0])\n",
+ " ds_e = finite_diff(fun, e, de) # dS_e de\n",
+ " #\n",
+ " ds = ds_p0 + ds_e + ds_tf\n",
+ " return s, ds\n",
+ "\n",
+ "@tools.tensorize(dhomfun, tvars=(1, 2, 3), full=True)\n",
+ "def homfun(p0, e, tf):\n",
+ " xf, pf = f(t0, x0, p0, tf, e) # We use the flow to get z(tf, x0, p0, e)\n",
+ " s = xf - xf_target # x(tf, x0, p0) - xf_target\n",
+ " return s"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x,pars)| |x| Homotopic param Arclength s det A(s) Dot product \n",
+ " \n",
+ " 1 2.22044605e-16 2.20554898009e+00 1.00000000000e+00 0.00000000e+00 -3.99453543e-01 0.00000000e+00\n",
+ " 2 2.22044605e-16 2.19703976141e+00 9.93456169329e-01 1.07344549e-02 -4.02221666e-01 9.99999991e-01\n",
+ " 3 3.33066907e-16 2.17562949518e+00 9.76983031043e-01 3.77485955e-02 -4.09360819e-01 9.99999942e-01\n",
+ " 4 2.22044605e-16 2.13582370908e+00 9.46324313715e-01 8.79925768e-02 -4.23336260e-01 9.99999773e-01\n",
+ " 5 0.00000000e+00 2.04380511707e+00 8.75274200125e-01 2.04248946e-01 -4.59644793e-01 9.99998415e-01\n",
+ " 6 1.11022302e-16 1.92916643462e+00 7.86347624598e-01 3.49335047e-01 -5.14727915e-01 9.99996190e-01\n",
+ " 7 2.22044605e-16 1.79444755857e+00 6.81092176321e-01 5.20296827e-01 -5.99279037e-01 9.99990735e-01\n",
+ " 8 1.11022302e-16 1.66966322809e+00 5.82619647458e-01 6.79256037e-01 -7.06991902e-01 9.99985113e-01\n",
+ " 9 1.11022302e-16 1.56620772374e+00 5.00008221016e-01 8.11648417e-01 -8.30695653e-01 9.99981810e-01\n",
+ " 10 3.33066907e-16 1.46593779252e+00 4.18824463927e-01 9.40663687e-01 -9.99327396e-01 9.99971770e-01\n",
+ " 11 0.00000000e+00 1.37678846132e+00 3.45480162266e-01 1.05610658e+00 -1.21575495e+00 9.99967683e-01\n",
+ " 12 5.55111512e-17 1.28960342151e+00 2.72548876780e-01 1.16977396e+00 -1.52984851e+00 9.99968620e-01\n",
+ " 13 1.11022302e-16 1.23722039409e+00 2.28228170219e-01 1.23839109e+00 -1.79572280e+00 9.99995132e-01\n",
+ " 14 7.77156117e-16 1.19422849087e+00 1.91735175890e-01 1.29478295e+00 -2.07744292e+00 9.99999997e-01\n",
+ " 15 8.88178420e-16 1.15761257447e+00 1.60763287717e-01 1.34274112e+00 -2.37832445e+00 9.99993905e-01\n",
+ " 16 8.88178420e-16 1.12621332813e+00 1.34479524463e-01 1.38368932e+00 -2.69537295e+00 9.99976683e-01\n",
+ " 17 6.66133815e-16 1.09882012933e+00 1.11936744078e-01 1.41916572e+00 -3.03058070e+00 9.99950610e-01\n",
+ " 18 9.43689571e-16 1.07488689408e+00 9.26897526120e-02 1.44987824e+00 -3.38245451e+00 9.99920746e-01\n",
+ " 19 3.10862447e-15 1.05162281210e+00 7.45308292960e-02 1.47939067e+00 -3.79520044e+00 9.99862606e-01\n",
+ " 20 4.44089210e-16 1.03348997369e+00 6.08568585866e-02 1.50210166e+00 -4.18199975e+00 9.99863622e-01\n",
+ " 21 7.77156117e-16 1.01743621699e+00 4.91774488730e-02 1.52195467e+00 -4.58879415e+00 9.99842046e-01\n",
+ " 22 2.88657986e-15 1.00351364714e+00 3.94278240330e-02 1.53895177e+00 -5.00712133e+00 9.99833210e-01\n",
+ " 23 1.11022302e-15 9.91189285569e-01 3.11338118442e-02 1.55380731e+00 -5.44570207e+00 9.99823057e-01\n",
+ " 24 7.21644966e-16 9.80356390822e-01 2.41377538128e-02 1.56670310e+00 -5.90269325e+00 9.99819071e-01\n",
+ " 25 1.11022302e-16 9.70835442114e-01 1.82431398575e-02 1.57790126e+00 -6.37956456e+00 9.99817622e-01\n",
+ " 26 8.99280650e-15 9.62692462871e-01 1.34115980809e-02 1.58736986e+00 -6.86424447e+00 9.99827368e-01\n",
+ " 27 4.77395901e-15 9.55675551884e-01 9.42082903289e-03 1.59544235e+00 -7.36122521e+00 9.99834372e-01\n",
+ " 28 1.32116540e-14 9.49853651601e-01 6.24486269889e-03 1.60207427e+00 -7.85282352e+00 9.99851794e-01\n",
+ " 29 4.19664303e-14 9.45389069838e-01 3.90225115046e-03 1.60711617e+00 -8.30049315e+00 9.99886223e-01\n",
+ " 30 1.88737914e-15 9.41931793716e-01 2.15059352872e-03 1.61099191e+00 -8.71023410e+00 9.99909978e-01\n",
+ " 31 6.66133815e-16 9.41628939496e-01 2.00000000000e-03 1.61133013e+00 -8.74973421e+00 9.99999182e-01\n",
+ "\n",
+ " Results of the path solver method:\n",
+ "\n",
+ " xf = [-0.94162894]\n",
+ " parsf = 0.002\n",
+ " |f(xf,parsf)| = 6.661338147750939e-16\n",
+ " steps = 31\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Homotopy successfully completed.\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Making the penalization smaller: homotopy on e\n",
+ "p0 = sol_nle.x\n",
+ "sol_path_e = nt.path.solve(homfun, p0, e_init, e_final, args=tf_init, df=homfun)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 3 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot solution for (tf, e) = (tf_init, e_final)\n",
+ "plotSolution(sol_path_e.xf, e_final, tf_init)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x,pars)| |x| Homotopic param Arclength s det A(s) Dot product \n",
+ " \n",
+ " 1 2.22044605e-16 9.41628939496e-01 1.00000000000e+00 0.00000000e+00 4.01455484e+00 0.00000000e+00\n",
+ " 2 8.88178420e-16 9.44075168781e-01 1.00970881514e+00 1.00122571e-02 4.08611419e+00 9.99990245e-01\n",
+ " 3 6.66133815e-16 9.52110673458e-01 1.04297202177e+00 4.42326128e-02 4.35312513e+00 9.99884749e-01\n",
+ " 4 8.88178420e-16 9.61556842283e-01 1.08526416490e+00 8.75675217e-02 4.75042396e+00 9.99811995e-01\n",
+ " 5 5.55111512e-17 9.71896630561e-01 1.13674411999e+00 1.40076814e-01 5.34799409e+00 9.99719724e-01\n",
+ " 6 5.55111512e-16 9.81245191618e-01 1.18988053242e+00 1.94030671e-01 6.14816857e+00 9.99701750e-01\n",
+ " 7 2.22044605e-15 9.89208695747e-01 1.24261341184e+00 2.47362758e-01 7.21580053e+00 9.99709964e-01\n",
+ " 8 7.21644966e-16 9.95584144595e-01 1.29272773597e+00 2.97882063e-01 8.62227225e+00 9.99745289e-01\n",
+ " 9 1.22124533e-15 1.00051725716e+00 1.33956581293e+00 3.44980041e-01 1.04922584e+01 9.99787850e-01\n",
+ " 10 1.88737914e-15 1.00422155325e+00 1.38281120954e+00 3.88384407e-01 1.30075715e+01 9.99831827e-01\n",
+ " 11 2.33146835e-15 1.00693858544e+00 1.42255002654e+00 4.28216425e-01 1.64500266e+01 9.99872114e-01\n",
+ " 12 4.88498131e-15 1.00888895880e+00 1.45901756959e+00 4.64736370e-01 2.12529132e+01 9.99906881e-01\n",
+ " 13 1.22124533e-14 1.01026195185e+00 1.49256266733e+00 4.98309736e-01 2.80968027e+01 9.99935247e-01\n",
+ " 14 4.94049246e-15 1.01121117641e+00 1.52358925456e+00 5.29350951e-01 3.80663163e+01 9.99957193e-01\n",
+ " 15 6.59472477e-14 1.01185675334e+00 1.55253698600e+00 5.58305944e-01 5.29258454e+01 9.99973207e-01\n",
+ " 16 8.80406859e-14 1.01228937436e+00 1.57986254022e+00 5.85634959e-01 7.56112643e+01 9.99984175e-01\n",
+ " 17 1.68531855e-13 1.01257542227e+00 1.60602989124e+00 6.11803893e-01 1.11142150e+02 9.99991198e-01\n",
+ " 18 2.80664381e-13 1.01276214622e+00 1.63150346762e+00 6.37278163e-01 1.68372602e+02 9.99995395e-01\n",
+ " 19 2.86659585e-13 1.01288241210e+00 1.65674705661e+00 6.62522043e-01 2.63490945e+02 9.99997737e-01\n",
+ " 20 2.96984659e-13 1.01295868532e+00 1.68222816553e+00 6.88003269e-01 4.27333674e+02 9.99998957e-01\n",
+ " 21 1.11244347e-13 1.01300613907e+00 1.70842815072e+00 7.14203298e-01 7.21468310e+02 9.99999552e-01\n",
+ " 22 4.27813340e-12 1.01303494245e+00 1.73585852757e+00 7.41633690e-01 1.27569212e+03 9.99999821e-01\n",
+ " 23 2.57732169e-11 1.01305187229e+00 1.76508420787e+00 7.70859375e-01 2.38160109e+03 9.99999935e-01\n",
+ " 24 1.20242538e-10 1.01306141530e+00 1.79675602397e+00 8.02531193e-01 4.74536748e+03 9.99999978e-01\n",
+ " 25 6.23208152e-10 1.01306651002e+00 1.83165732709e+00 8.37432497e-01 1.02379807e+04 9.99999994e-01\n",
+ " 26 3.66588537e-09 1.01306904469e+00 1.87077329303e+00 8.76548463e-01 2.43881436e+04 9.99999998e-01\n",
+ " 27 2.69244553e-08 1.01307019491e+00 1.91539837246e+00 9.21173542e-01 6.58870660e+04 1.00000000e+00\n",
+ " 28 2.69732114e-07 1.01307065731e+00 1.96730883161e+00 9.73084001e-01 2.09516626e+05 1.00000000e+00\n",
+ " 29 2.15117862e-06 1.01307076680e+00 2.00000000000e+00 1.00577516e+00 4.36713283e+05 1.00000000e+00\n",
+ "\n",
+ " Results of the path solver method:\n",
+ "\n",
+ " xf = [-1.01307077]\n",
+ " parsf = 2.0\n",
+ " |f(xf,parsf)| = 2.1511786191807936e-06\n",
+ " steps = 29\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Homotopy successfully completed.\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Making the time bigger: homotopy on tf\n",
+ "p0 = sol_path_e.xf # sol is coming from last homotopy\n",
+ "pathfun = lambda p0, tf, e: homfun(p0, e, tf) # invert order of arguments\n",
+ "sol_path_tf = nt.path.solve(pathfun, p0, tf_init, tf_final, args=e_final, df=pathfun)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 3 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot solution for (tf, e) = (tf_final, e_final)\n",
+ "plotSolution(sol_path_tf.xf, e_final, tf_final)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## III) Resolution of the optimal control problem by multiple shooting"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We come back to the original optimal control problem:\n",
+ "\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\int_0^{t_f} x^2(t) \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = f(x(t), u(t)) := \\displaystyle u(t), \\quad |u(t)| \\le 1, \\quad t \\in [0, t_f] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = 1, \\quad x(t_f) = 1/2.\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "We have determined that the optimal control follows the strategy:\n",
+ "\n",
+ "$$\n",
+ " u(t) = \\left\\{ \n",
+ " \\begin{array}{lll}\n",
+ " -1 & \\text{if} & t \\in [0, t_1], \\\\[0.5em]\n",
+ " \\phantom{-}0 & \\text{if} & t \\in (t_1, t_2], \\\\[0.5em]\n",
+ " +1 & \\text{if} & t \\in (t_2, t_f],\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "with $0 < t_1 < t_2 < t_f=2$. \n",
+ "\n",
+ "\n",
+ "<div class=\"alert alert-warning\">\n",
+ "\n",
+ "**Goal**\n",
+ "\n",
+ "The goal is to find the values of the switching times $t_1$ and $t_2$ together with the initial covector $p_0$ (see Remark 2).\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Maximized Hamiltonian and its derivatives"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We define first the three control laws $u \\equiv \\{-1, 0, 1\\}$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Controls in feedback form\n",
+ "@tools.vectorize(vvars=(1, 2, 3))\n",
+ "def uplus(t, x, p):\n",
+ " u = +1.0\n",
+ " return u\n",
+ "\n",
+ "@tools.vectorize(vvars=(1, 2, 3))\n",
+ "def uminus(t, x, p):\n",
+ " u = -1.0\n",
+ " return u\n",
+ "\n",
+ "@tools.vectorize(vvars=(1, 2, 3))\n",
+ "def using(t, x, p):\n",
+ " u = 0.0\n",
+ " return u"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The pseudo-Hamiltonian is\n",
+ "\n",
+ "$$\n",
+ " H(x,p,u) = pu - x^2.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 4:_**\n",
+ " \n",
+ "Complete the code of the Hamiltonian for $u \\equiv +1$, with its derivatives.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Definition of the Hamiltonian and its derivatives for u = 1\n",
+ "def dhfunplus(t, x, dx, p, dp):\n",
+ " # dh = dh_x dx + dh_p dp\n",
+ "# hd = 0 ### TO COMPLETE: use uplus\n",
+ " u = uplus(t, x, p)\n",
+ " hd = u*dp - 2.0*x*dx\n",
+ " return hd\n",
+ " \n",
+ "def d2hfunplus(t, x, dx, d2x, p, dp, d2p):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ "# hdd = 0 ### TO COMPLETE\n",
+ " hdd = -2.0 * d2x * dx\n",
+ " return hdd\n",
+ "\n",
+ "@tools.tensorize(dhfunplus, d2hfunplus, tvars=(2, 3))\n",
+ "def hfunplus(t, x, p):\n",
+ "# h = 0 ### TO COMPLETE: use uplus\n",
+ " u = uplus(t, x, p)\n",
+ " h = p*u - x**2\n",
+ " return h\n",
+ "\n",
+ "hplus = ocp.Hamiltonian(hfunplus)\n",
+ "fplus = ocp.Flow(hplus)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Definition of the Hamiltonian and its derivatives for u = -1\n",
+ "def dhfunminus(t, x, dx, p, dp):\n",
+ " # dh = dh_x dx + dh_p dp\n",
+ " u = uminus(t, x, p)\n",
+ " hd = u*dp - 2.0*x*dx\n",
+ " return hd\n",
+ " \n",
+ "def d2hfunminus(t, x, dx, d2x, p, dp, d2p):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ " hdd = -2.0 * d2x * dx\n",
+ " return hdd\n",
+ "\n",
+ "@tools.tensorize(dhfunminus, d2hfunminus, tvars=(2, 3))\n",
+ "def hfunminus(t, x, p):\n",
+ " u = uminus(t, x, p)\n",
+ " h = p*u - x**2\n",
+ " return h\n",
+ "\n",
+ "hminus = ocp.Hamiltonian(hfunminus)\n",
+ "fminus = ocp.Flow(hminus)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Definition of the Hamiltonian and its derivatives for u = 0\n",
+ "def dhfunsing(t, x, dx, p, dp):\n",
+ " # dh = dh_x dx + dh_p dp\n",
+ " u = using(t, x, p)\n",
+ " hd = u*dp - 2.0*x*dx\n",
+ " return hd\n",
+ " \n",
+ "def d2hfunsing(t, x, dx, d2x, p, dp, d2p):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ " hdd = -2.0 * d2x * dx\n",
+ " return hdd\n",
+ "\n",
+ "@tools.tensorize(dhfunsing, d2hfunsing, tvars=(2, 3))\n",
+ "def hfunsing(t, x, p):\n",
+ " u = using(t, x, p)\n",
+ " h = p*u - x**2\n",
+ " return h\n",
+ "\n",
+ "hsing = ocp.Hamiltonian(hfunsing)\n",
+ "fsing = ocp.Flow(hsing)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Shooting function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The multiple shooting function is given by\n",
+ "\n",
+ "$$\n",
+ " S(p_0, t_1, t_2) := \n",
+ " \\begin{pmatrix}\n",
+ " x(t_1, t_0, x_0, p_0, u_-) \\\\\n",
+ " p(t_1, t_0, x_0, p_0, u_-) \\\\\n",
+ " x(t_f, t_2, x_2, p_2, u_+)\n",
+ " \\end{pmatrix},\n",
+ "$$\n",
+ "\n",
+ "where $z_2 := (x_2, p_2) = z(t_2, t_1, x_1, p_1, u_0)$, $z_1 := (x_1, p_1) = z(t_1, t_0, x_0, p_0, u_-)$ and where z(t, s, a, b, u) is the solution at time $t$ of the Hamiltonian system associated to the control u starting at time $s$ at the initial condition $z(s) = (a,b)$.\n",
+ "\n",
+ "We have introduced the notation $u_-$ for $u\\equiv -1$, $u_0$ for $u\\equiv 0$ and $u_+$ for $u\\equiv +1$.\n",
+ "\n",
+ "**_Remark:_** We know that $(x_2, p_2)=(0,0)$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 5:_**\n",
+ " \n",
+ "Complete the code of the multiple shooting function.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "tf = tf_final\n",
+ "\n",
+ "def shoot_multiple(y):\n",
+ " p0 = y[0]\n",
+ " t1 = y[1]\n",
+ " t2 = y[2]\n",
+ " \n",
+ "# s = np.zeros([3]) ### TO COMPLETE: use fminus, fsin, fplus, t0, x0, xf_target\n",
+ " \n",
+ " x1, p1 = fminus(t0, x0, p0, t1) # on [ 0, t1]\n",
+ " x2, p2 = (np.array([0.0]), np.array([0.0])) #fsing(t1, x1, p1, t2) # on [t1, t2]\n",
+ " xf, pf = fplus(t2, x2, p2, tf) # on [t2, tf]\n",
+ " \n",
+ " s = np.zeros([3])\n",
+ " s[0] = x1\n",
+ " s[1] = p1\n",
+ " s[2] = xf - xf_target # x(tf, x0, p0) - xf_target\n",
+ " return s"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Shooting"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "y_guess = [-1.01307077 0.9 1.6 ] \n",
+ "\n",
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 1.432908241330024e-01 2.096738509815576e+00\n",
+ " 2 9.999998053989939e-03 2.066422027958497e+00\n",
+ " 3 1.506856008950395e-05 2.061545503561054e+00\n",
+ " 4 1.103251344504288e-11 2.061552812803479e+00\n",
+ " 5 3.854837484910665e-16 2.061552812808831e+00\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [-1. 1. 1.5]\n",
+ " f(xsol) = [ 1.38777878e-17 3.47378376e-16 -1.66533454e-16]\n",
+ " nfev = 5\n",
+ " njev = 1\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "p0_guess = sol_path_tf.xf # from previous homotopy\n",
+ "t1_guess = 0.9 # to update\n",
+ "t2_guess = 1.6 # to update\n",
+ "y_guess = np.array([float(p0_guess), t1_guess, t2_guess])\n",
+ "\n",
+ "print('y_guess = ', y_guess, '\\n')\n",
+ "\n",
+ "if tf>=2.0:\n",
+ " sol_nle_mul = nt.nle.solve(shoot_multiple, y_guess)\n",
+ "else:\n",
+ " print('Warning: tf should be greater or equal to 2')\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# function to plot solution\n",
+ "\n",
+ "def plotSolutionBSB(p0, t1, t2, tf):\n",
+ "\n",
+ " N = 20\n",
+ " \n",
+ " tspan1 = list(np.linspace(t0, t1, N+1))\n",
+ " tspan2 = list(np.linspace(t1, t2, N+1))\n",
+ " tspanf = list(np.linspace(t2, tf, N+1))\n",
+ " \n",
+ " x1, p1 = fminus(t0, x0, p0, tspan1) # on [ 0, t1]\n",
+ " x2, p2 = fsing(t1, x1[-1], p1[-1], tspan2) # on [t1, t2]\n",
+ " xf, pf = fplus(t2, x2[-1], p2[-1], tspanf) # on [t2, tf]\n",
+ " \n",
+ " u1 = uminus(tspan1, x1, p1)\n",
+ " u2 = using(tspan2, x2, p2)\n",
+ " uf = uplus(tspanf, xf, pf)\n",
+ "\n",
+ " fig = plt.figure()\n",
+ " ax = fig.add_subplot(511); ax.plot(tspan1, x1); ax.plot(tspan2, x2); ax.plot(tspanf, xf); \n",
+ " ax.set_xlabel('t'); ax.set_ylabel('$x$'); ax.axhline(0, color='k')\n",
+ " ax = fig.add_subplot(513); ax.plot(tspan1, p1); ax.plot(tspan2, p2); ax.plot(tspanf, pf);\n",
+ " ax.set_xlabel('t'); ax.set_ylabel('$p$'); ax.axhline(0, color='k')\n",
+ " ax = fig.add_subplot(515); ax.plot(tspan1, u1); ax.plot(tspan2, u2); ax.plot(tspanf, uf);\n",
+ " ax.set_xlabel('t'); ax.set_ylabel('$u$'); ax.axhline(0, color='k')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 3 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot solution\n",
+ "p0 = sol_nle_mul.x[0]\n",
+ "t1 = sol_nle_mul.x[1]\n",
+ "t2 = sol_nle_mul.x[2]\n",
+ "plotSolutionBSB(p0, t1, t2, tf)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/doc/exercices/simple_shooting_application.ipynb b/doc/exercices/simple_shooting_application.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..2e60c327e4ce1d92d7550bd3a3ec7b4a913b0c65
--- /dev/null
+++ b/doc/exercices/simple_shooting_application.ipynb
@@ -0,0 +1,670 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solving by simple shooting the energy min 2D integrator problem with friction and transversality conditions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Author: Olivier Cots\n",
+ "* Date: March 2021\n",
+ "\n",
+ "------"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Consider the following optimal control problem (Lagrange cost, fixed final time):\n",
+ "\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\frac{1}{2} \\int_0^{1} u^2(t) \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = (x_2(t), -\\mu x_2^2(t) + u(t)), \\quad u(t) \\in \\mathrm{R}, \\quad t \\in [0, 1] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = (-1, 0), \\quad c(x(1)) = 0.\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "We will consider two cases:\n",
+ "\n",
+ "$$\n",
+ "a)~ c(x) = x - (1, 0), \\quad b)~ c(x) = x_1 - 1.\n",
+ "$$\n",
+ "\n",
+ "We consider the normal case ($p^0 = -1$), so the pseudo-Hamiltonian of the problem is\n",
+ "\n",
+ "$$\n",
+ " H(x,p,u) = p_1 x_2 + p_2 (-\\mu x_2^2 + u) - \\frac{1}{2} u^2.\n",
+ "$$\n",
+ "\n",
+ "We denote by $t_0$, $t_f$ and $x_0$ the initial time, final time and initial condition.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-warning\">\n",
+ "\n",
+ "**Goal**\n",
+ "\n",
+ "Solve the cases a) and b) of this optimal control problem by simple shooting with the nutopy package.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**_Remark._** \n",
+ "* See this [page](https://ct.gitlabpages.inria.fr/gallery/shooting_tutorials/simple_shooting_general.html) for a general presentation of the simple shooting method with the use of nutopy package. \n",
+ "* See this [page](https://ct.gitlabpages.inria.fr/gallery/smooth_case/smooth_case.html) for a more detailed use of nutopy package on a smooth example. \n",
+ "* See this [page](https://ct.gitlabpages.inria.fr/nutopy/) for the documention of nutopy package."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Preliminaries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# import packages\n",
+ "import nutopy as nt\n",
+ "import nutopy.tools as tools\n",
+ "import nutopy.ocp as ocp\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "#plt.rcParams['figure.figsize'] = [10, 5]\n",
+ "plt.rcParams['figure.dpi'] = 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# parameters\n",
+ "t0 = 0.0 # initial time\n",
+ "tf = 1.0 # final time\n",
+ "x0 = np.array([-1.0, 0.0]) # initial condition\n",
+ "xf_target_a = np.array([1.0, 0.0]) # final target for the case a\n",
+ "xf_target_b = np.array([1.0]) # final target for the case b\n",
+ "mu = 0.5 # parameter mu"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Questions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 1:_**\n",
+ " \n",
+ "Write the maximizing control in feeback form $u[p]$.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Answer 1:** To complete here (double-click on the line to complete)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 2:_**\n",
+ " \n",
+ "Complete the code of `ufun` coding the control in feedback form.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 2 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# Control in feedback form: used for plotting\n",
+ "#\n",
+ "@tools.vectorize(vvars=(1,))\n",
+ "def ufun(p):\n",
+ "# u = 0 ### TO COMPLETE\n",
+ " u = p[1] # u = p2\n",
+ " return u"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 3:_**\n",
+ " \n",
+ "Write the maximized Hamiltonian and the adjoint equation.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Answer 3:** To complete here (double-click on the line to complete)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 4:_**\n",
+ " \n",
+ "Complete the code of `hfun` and `dhfun` coding the maximized Hamiltonian and its derivative.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**_Remark._** Let us denote by $h(t, x, p) = H(x, p, u[p])$ the maximized Hamiltonian. The function `dhfun` codes:\n",
+ "\n",
+ "$$\n",
+ " \\frac{\\partial h}{\\partial x}(t, x, p) \\cdot \\delta x + \\frac{\\partial h}{\\partial p}(t, x, p) \\cdot \\delta p.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The (normal and maximized) Hamiltonian is straightforwardly implemented in `hfun`. For further needs, we have to implement its first and second derivatives _wrt._ to state ($x$) and costate ($p$). This derivatives, evaluated against first and second order increments are implemented by `dhfun` and `d2hfun`, respectively."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 4 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# Maximized Hamiltonian with its derivative\n",
+ "#\n",
+ "def hfun(t, x, p):\n",
+ " '''\n",
+ " Hamiltonian: \n",
+ " \n",
+ " h = hfun(t, x, p, mu)\n",
+ " \n",
+ " Inputs: \n",
+ " \n",
+ " - t : time, float\n",
+ " - x : state, array\n",
+ " - p : co-state, array\n",
+ " - mu : friction parameter, float\n",
+ " \n",
+ " Outputs:\n",
+ " \n",
+ " - h : Hamiltonian, float\n",
+ " \n",
+ " '''\n",
+ " x2 = x[1]\n",
+ " p1 = p[0]\n",
+ " p2 = p[1]\n",
+ "# h = 0.0 ### TO COMPLETE\n",
+ " h = p1*x2-mu*x2**2*p2+0.5*p2**2 \n",
+ " return h\n",
+ "\n",
+ "def dhfun(t, x, dx, p, dp):\n",
+ " '''\n",
+ " Derivative of the Hamiltonian: \n",
+ " \n",
+ " hd = dhfun(t, x, dx, p, dp, mu)\n",
+ " \n",
+ " Inputs: \n",
+ " \n",
+ " - t : time, float\n",
+ " - x : state, array\n",
+ " - dx : state increment, array\n",
+ " - p : co-state, array\n",
+ " - dp : co-state increment, array\n",
+ " - mu : friction parameter, float\n",
+ " \n",
+ " Outputs:\n",
+ " \n",
+ " - hd : derivative of the Hamiltonian, float\n",
+ " \n",
+ " '''\n",
+ " x2 = x[1]\n",
+ " dx2 = dx[1]\n",
+ " p1 = p[0]\n",
+ " p2 = p[1]\n",
+ " dp1 = dp[0]\n",
+ " dp2 = dp[1]\n",
+ "# hd = 0.0 ### TO COMPLETE\n",
+ " hd = dp1*x2+p1*dx2-2.0*mu*x2*dx2*p2-mu*x2**2*dp2+p2*dp2\n",
+ " return hd"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# The second order derivative of hfun and the definition of the flow\n",
+ "#\n",
+ "def d2hfun(t, x, dx, d2x, p, dp, d2p):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ " x2 = x[1]\n",
+ " dx2 = dx[1]\n",
+ " d2x2 = d2x[1]\n",
+ " p1 = p[0]\n",
+ " p2 = p[1]\n",
+ " dp1 = dp[0]\n",
+ " dp2 = dp[1]\n",
+ " d2p1 = d2p[0]\n",
+ " d2p2 = d2p[1]\n",
+ " hdd = dp1*d2x2 \\\n",
+ " + d2p1*dx2 \\\n",
+ " - 2.0*mu*d2x2*dx2*p2 - 2.0*mu*x2*dx2*d2p2 \\\n",
+ " - 2.0*mu*x2*d2x2*dp2 \\\n",
+ " + d2p2*dp2\n",
+ " return hdd\n",
+ "\n",
+ "hfun = nt.tools.tensorize(dhfun, d2hfun, tvars=(2, 3))(hfun)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "h = ocp.Hamiltonian(hfun) # The Hamiltonian object"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To define in the following the shooting function, one must integrate the Hamiltonian system defined by `h`. This is done by defining a [Flow](https://ct.gitlabpages.inria.fr/nutopy/api/ocp.html#nutopy.ocp.Flow) object:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "f = ocp.Flow(h) # The flow associated to the Hamiltonian object is \n",
+ " # the exponential mapping with its derivative\n",
+ " # that can be used to define the Jacobian of the \n",
+ " # shooting function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To compute the value of the Hamiltonan flow at time $t_f$ starting from time $t_0$ and initial conditions $(x_0,p_0)$, do the following:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[-0.96666508 0.05000781] [0.1 0.00127897]\n"
+ ]
+ }
+ ],
+ "source": [
+ "p0 = np.array([0.1, 0.1])\n",
+ "xf, pf = f(t0, x0, p0, tf)\n",
+ "print(xf, pf)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### case a: $c(x) = x - x_f$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this case, the shooting function is simply given by\n",
+ "\n",
+ "$$\n",
+ " S(p_0) = \\pi_x(z(t_f, t_0, x_0, p_0)) - x_f,\n",
+ "$$\n",
+ "\n",
+ "where $x_f = (1, 0)$ and $z(t_f, t_0, x_0, p_0)$ is the value of the Hamiltonan flow at time $t_f$ starting from time $t_0$ and initial conditions $(x_0,p_0)$. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 5:_**\n",
+ " \n",
+ "Complete the code of `shoot` coding the shooting function.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 5 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# Shooting function and its derivative\n",
+ "#\n",
+ "# Nota bene: use f, t0, x0, tf, xf_target_a\n",
+ "#\n",
+ "\n",
+ "def shoot(p0):\n",
+ " '''\n",
+ " Shooting function\n",
+ " \n",
+ " s = S(p0)\n",
+ " \n",
+ " Inputs:\n",
+ " \n",
+ " p0 : initial co-state, array\n",
+ " \n",
+ " Outputs:\n",
+ " \n",
+ " s : value of the shooting function, array\n",
+ " '''\n",
+ "# s = zeros([2]) ### TO COMPLETE\n",
+ " xf, _ = f(t0, x0, p0, tf)\n",
+ " s = xf - xf_target_a\n",
+ " return s"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The Jacobian of $S$ at $p_0$ against the vector $\\delta p_0$ is given by:\n",
+ "\n",
+ "$$\n",
+ " S'(p_0) \\cdot \\delta p_0 = \\pi_x \\left(\\frac{\\partial z}{\\partial p_0}(t_f, t_0, x_0, p_0) \\cdot \\delta p_0 \\right) = \n",
+ " \\frac{\\partial x}{\\partial p_0}(t_f, t_0, x_0, p_0) \\cdot \\delta p_0.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Jacobian of the shooting function against dp0\n",
+ "def dshoot(p0, dp0):\n",
+ " (xf, dxf), _ = f(t0, x0, (p0, dp0), tf)\n",
+ " ds = dxf\n",
+ " return ds\n",
+ "\n",
+ "# We tensorize the shooting function, otherwise, we would have to give the Jacobian \n",
+ "# of S instead of the Jacobian against a vector, to the nle solver.\n",
+ "shoot = nt.tools.tensorize(dshoot)(shoot)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 1.967300768937284e+00 1.414213562373095e-01\n",
+ " 2 1.719731572785037e+00 1.798534093044436e+01\n",
+ " 3 1.410906422430211e+00 3.487107124079308e+01\n",
+ " 4 1.991207495319282e+00 3.937341638076422e+01\n",
+ " 5 7.277880985715982e-01 3.625515294040530e+01\n",
+ " 6 4.725619938021095e-01 3.555941926121004e+01\n",
+ " 7 3.166103150678147e-02 3.433969876028567e+01\n",
+ " 8 2.245063172754588e-03 3.442461252396225e+01\n",
+ " 9 6.943644107728013e-04 3.442864514091167e+01\n",
+ " 10 1.078577109865398e-04 3.442751328490402e+01\n",
+ " 11 2.201216767879966e-07 3.442730460220397e+01\n",
+ " 12 2.084484933152670e-09 3.442730418046803e+01\n",
+ " 13 1.938651563244826e-11 3.442730418446997e+01\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [31.89425568 12.96131661]\n",
+ " f(xsol) = [4.30899760e-12 1.89015747e-11]\n",
+ " nfev = 13\n",
+ " njev = 1\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ "p0_sol = [31.89425568 12.96131661] \t shoot = [4.30899760e-12 1.89015747e-11]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Resolution of the shooting function\n",
+ "#\n",
+ "p0_guess = np.array([0.1, 0.1])\n",
+ "sol = nt.nle.solve(shoot, p0_guess, df=shoot); p0_sol = sol.x\n",
+ "print('p0_sol =', p0_sol, '\\t shoot =', shoot(p0_sol))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Function to plot the solution\n",
+ "def plotSolution(p0):\n",
+ "\n",
+ " N = 100\n",
+ " tspan = list(np.linspace(t0, tf, N+1))\n",
+ " xf, pf = f(t0, x0, p0, tspan)\n",
+ " u = ufun(pf)\n",
+ "\n",
+ " fig = plt.figure()\n",
+ " ax = fig.add_subplot(711); ax.plot(tspan, xf); ax.set_xlabel('t'); ax.set_ylabel('$x$'); ax.axhline(0, color='k')\n",
+ " ax = fig.add_subplot(713); ax.plot(tspan, pf); ax.set_xlabel('t'); ax.set_ylabel('$p$'); ax.axhline(0, color='k')\n",
+ " ax = fig.add_subplot(715); ax.plot(tspan, u); ax.set_xlabel('t'); ax.set_ylabel('$u$'); ax.axhline(0, color='k')\n",
+ " \n",
+ " x1 = np.zeros(N+1)\n",
+ " x2 = np.zeros(N+1)\n",
+ " for i in range(0, N+1):\n",
+ " x1[i] = xf[i][0]\n",
+ " x2[i] = xf[i][1]\n",
+ " \n",
+ " ax = fig.add_subplot(717); ax.plot(x1, x2); ax.set_xlabel('x1'); ax.set_ylabel('$x2$'); ax.axhline(0, color='k')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 4 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot solution\n",
+ "plotSolution(p0_sol)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### case b: $c(x) = x_1 - 1$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 6:_**\n",
+ " \n",
+ "Give the transversality condition.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Answer 6:** To complete here (double-click on the line to complete)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 7:_**\n",
+ " \n",
+ "Write the shooting function.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Answer 7:** To complete here (double-click on the line to complete)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 8:_**\n",
+ " \n",
+ "Solve the shooting equations.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 8 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# Write the shooting function and its derivative\n",
+ "# Write the call to the nle solver\n",
+ "# Plot the solution\n",
+ "#\n",
+ "# Nota bene: use f, t0, x0, tf, xf_target_b\n",
+ "#"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/doc/exercices/simple_shooting_coding.ipynb b/doc/exercices/simple_shooting_coding.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..7df7b24b67cd4aed6ccbf6bc58d5b8d562d92289
--- /dev/null
+++ b/doc/exercices/simple_shooting_coding.ipynb
@@ -0,0 +1,1426 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Coding the indirect simple shooting method to solve the energy min 2D integrator problem with simple limit conditions and friction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Author: Olivier Cots\n",
+ "* Date: March 2021\n",
+ "\n",
+ "------"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Consider the following optimal control problem (Lagrange cost, fixed final time):\n",
+ "\n",
+ "$$ \n",
+ " \\left\\{ \n",
+ " \\begin{array}{l}\n",
+ " \\displaystyle J(u) := \\displaystyle \\frac{1}{2} \\int_0^{1} u^2(t) \\, \\mathrm{d}t \\longrightarrow \\min \\\\[1.0em]\n",
+ " \\dot{x}(t) = (x_2(t), -\\mu x_2^2(t) + u(t)), \\quad u(t) \\in \\mathrm{R}, \\quad t \\in [0, 1] \\text{ a.e.}, \\\\[1.0em]\n",
+ " x(0) = (-1, 0), \\quad x(1) = (1, 0).\n",
+ " \\end{array}\n",
+ " \\right. \n",
+ "$$\n",
+ "\n",
+ "We consider the normal case ($p^0 = -1$), so the pseudo-Hamiltonian of the problem is\n",
+ "\n",
+ "$$\n",
+ " H(x,p,u) = p_1 x_2 + p_2 (-\\mu x_2^2 + u) - \\frac{1}{2} u^2.\n",
+ "$$\n",
+ "\n",
+ "We denote by $t_0$, $t_f$ and $x_0$ the initial time, final time and initial condition.\n",
+ "\n",
+ "<div class=\"alert alert-warning\">\n",
+ "\n",
+ "**Main goal**\n",
+ "\n",
+ "Code the simple shooting method to solve this optimal control problem.\n",
+ " \n",
+ "</div>\n",
+ "\n",
+ "Steps:\n",
+ "\n",
+ "1. Use nutopy package to solve the problem: see this [page](https://ct.gitlabpages.inria.fr/gallery/shooting_tutorials/simple_shooting_general.html) for a general presentation of the simple shooting method with the use of nutopy package. See this [page](https://ct.gitlabpages.inria.fr/gallery/smooth_case/smooth_case.html) for a more detailed use of nutopy package on a smooth example.\n",
+ "2. Replace the [numerical integrator](https://en.wikipedia.org/w/index.php?title=Numerical_integration&oldid=1000975450). It is asked to code Euler (order 1) and Runge (order 2) methods and a Runge-Kutta method of order 4.\n",
+ "3. Replace the [Newton solver](https://en.wikipedia.org/wiki/Newton%27s_method). It is asked to code a simple version of a Newton solver."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Preliminaries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Import packages\n",
+ "#\n",
+ "import nutopy as nt\n",
+ "import nutopy.tools as tools\n",
+ "import nutopy.ocp as ocp\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "plt.rcParams['figure.dpi'] = 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Parameters\n",
+ "# This parameters are used all through the notebook.\n",
+ "#\n",
+ "t0 = 0.0 # initial time\n",
+ "tf = 1.0 # final time\n",
+ "x0 = np.array([-1.0, 0.0]) # initial condition\n",
+ "xf_target = np.array([1.0, 0.0]) # final target\n",
+ "mu = 0.5 # friction parameter\n",
+ "dimx = x0.shape[0] # dimension of the state space"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Step 1: Resolution of the shooting function with nutopy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The maximized Hamiltonian is\n",
+ "\n",
+ "$$\n",
+ " h(x, p) = H(x, p, u[x, p]) = x_2 p_1 - \\mu x_2^2 p_2 + \\frac{1}{2} p_2^2, \\quad z = (x, p),\n",
+ "$$\n",
+ "\n",
+ "where $u[x, p] = p_2$ is the maximizing control in feedback form."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Maximized Hamiltonian with its derivatives and its flow\n",
+ "def hfun(t, x, p):\n",
+ " x2 = x[1]\n",
+ " p1 = p[0]\n",
+ " p2 = p[1]\n",
+ " h = p1*x2-mu*x2**2*p2+0.5*p2**2 \n",
+ " return h\n",
+ "\n",
+ "def dhfun(t, x, dx, p, dp):\n",
+ " x2 = x[1]\n",
+ " dx2 = dx[1]\n",
+ " p1 = p[0]\n",
+ " p2 = p[1]\n",
+ " dp1 = dp[0]\n",
+ " dp2 = dp[1]\n",
+ " hd = dp1*x2+p1*dx2-2.0*mu*x2*dx2*p2-mu*x2**2*dp2+p2*dp2\n",
+ " return hd\n",
+ "\n",
+ "def d2hfun(t, x, dx, d2x, p, dp, d2p):\n",
+ " # d2h = dh_xx dx d2x + dh_xp dp d2x + dh_px dx d2p + dh_pp dp d2p\n",
+ " x2 = x[1]\n",
+ " dx2 = dx[1]\n",
+ " d2x2 = d2x[1]\n",
+ " p1 = p[0]\n",
+ " p2 = p[1]\n",
+ " dp1 = dp[0]\n",
+ " dp2 = dp[1]\n",
+ " d2p1 = d2p[0]\n",
+ " d2p2 = d2p[1]\n",
+ " hdd = dp1*d2x2 \\\n",
+ " + d2p1*dx2 \\\n",
+ " - 2.0*mu*d2x2*dx2*p2 - 2.0*mu*x2*dx2*d2p2 \\\n",
+ " - 2.0*mu*x2*d2x2*dp2 \\\n",
+ " + d2p2*dp2\n",
+ " return hdd\n",
+ "\n",
+ "hfun = nt.tools.tensorize(dhfun, d2hfun, tvars=(2, 3))(hfun)\n",
+ "h = ocp.Hamiltonian(hfun) # The Hamiltonian object\n",
+ "f = ocp.Flow(h) # The flow associated to the Hamiltonian object is \n",
+ " # the exponential mapping with its derivative\n",
+ " # that can be used to define the Jacobian of the \n",
+ " # shooting function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The shooting function is given by\n",
+ "\n",
+ "$$\n",
+ " S(p_0) = \\pi_x(z(t_f, x_0, p_0)) - x_f,\n",
+ "$$\n",
+ "\n",
+ "where $x_f = (1, 0)$ is the target, where $\\pi_x(x,p) := x$ is the canonical projection into the state space and where $z(t_f, x_0, p_0)$ is the solution at time $t_f$ of \n",
+ "\n",
+ "$$\n",
+ " \\dot{z}(t) = \\vec{H}(z(t), u[z(t)]) = \\vec{h}(z(t)), \\quad z(0) = (x_0, p_0),\n",
+ "$$\n",
+ "\n",
+ "with $\\vec{H}(z, u) := (\\nabla_p H(z,u), -\\nabla_x H(z,u))$ and $\\vec{h}(z) := (\\nabla_p h(z), -\\nabla_x h(z))$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Shooting function and its derivative\n",
+ "def dshoot(p0, dp0):\n",
+ " (xf, dxf), _ = f(t0, x0, (p0, dp0), tf)\n",
+ " s = xf - xf_target # code duplication (in order to compute dxf, shooting also needs to compute xf;\n",
+ " # accordingly, full=True)\n",
+ " ds = dxf\n",
+ " return s, ds\n",
+ "\n",
+ "@tools.tensorize(dshoot, full=True)\n",
+ "def shoot(p0):\n",
+ " xf, _ = f(t0, x0, p0, tf)\n",
+ " s = xf - xf_target\n",
+ " return s"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We solve with the nutopy package\n",
+ "$$\n",
+ " S(p_0) = 0.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 1.967300768937284e+00 1.414213562373095e-01\n",
+ " 2 1.719731572785037e+00 1.798534093044436e+01\n",
+ " 3 1.410906422430211e+00 3.487107124079308e+01\n",
+ " 4 1.991207495319282e+00 3.937341638076422e+01\n",
+ " 5 7.277880985715982e-01 3.625515294040530e+01\n",
+ " 6 4.725619938021095e-01 3.555941926121004e+01\n",
+ " 7 3.166103150678147e-02 3.433969876028567e+01\n",
+ " 8 2.245063172754588e-03 3.442461252396225e+01\n",
+ " 9 6.943644107728013e-04 3.442864514091167e+01\n",
+ " 10 1.078577109865398e-04 3.442751328490402e+01\n",
+ " 11 2.201216767879966e-07 3.442730460220397e+01\n",
+ " 12 2.084484933152670e-09 3.442730418046803e+01\n",
+ " 13 1.938651563244826e-11 3.442730418446997e+01\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [31.89425568 12.96131661]\n",
+ " f(xsol) = [4.30899760e-12 1.89015747e-11]\n",
+ " nfev = 13\n",
+ " njev = 1\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ " p0_nutopy = [31.89425568 12.96131661] \n",
+ " shoot(p0_nutopy) = [4.30899760e-12 1.89015747e-11]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Resolution of the shooting function S(p0) = 0\n",
+ "#\n",
+ "p0_guess = np.array([0.1, 0.1])\n",
+ "sol = nt.nle.solve(shoot, p0_guess, df=shoot); p0_nutopy = sol.x\n",
+ "print(' p0_nutopy =', p0_nutopy, \\\n",
+ " '\\n shoot(p0_nutopy) =', shoot(p0_nutopy))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Functions needed to plot the solution\n",
+ "@tools.vectorize(vvars=(1,))\n",
+ "def ufun(p):\n",
+ " u = p[1] # u = p2\n",
+ " return u\n",
+ "\n",
+ "def plotSolution(p0):\n",
+ "\n",
+ " N = 100\n",
+ " tspan = list(np.linspace(t0, tf, N+1))\n",
+ " xf, pf = f(t0, x0, p0, tspan)\n",
+ " u = ufun(pf)\n",
+ "\n",
+ " fig = plt.figure()\n",
+ " ax = fig.add_subplot(711); ax.plot(tspan, xf); ax.set_xlabel('t'); ax.set_ylabel('$x$'); ax.axhline(0, color='k')\n",
+ " ax = fig.add_subplot(713); ax.plot(tspan, pf); ax.set_xlabel('t'); ax.set_ylabel('$p$'); ax.axhline(0, color='k')\n",
+ " ax = fig.add_subplot(715); ax.plot(tspan, u); ax.set_xlabel('t'); ax.set_ylabel('$u$'); ax.axhline(0, color='k')\n",
+ " \n",
+ " x1 = np.zeros(N+1)\n",
+ " x2 = np.zeros(N+1)\n",
+ " for i in range(0, N+1):\n",
+ " x1[i] = xf[i][0]\n",
+ " x2[i] = xf[i][1]\n",
+ " \n",
+ " ax = fig.add_subplot(717); ax.plot(x1, x2); ax.set_xlabel('x1'); ax.set_ylabel('$x2$'); ax.axhline(0, color='k')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 4 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot solution\n",
+ "plotSolution(p0_nutopy)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Step 2: Replacing the numerical integrator"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us consider an Initial Value Problem (IVP) or Cauchy problem of the form\n",
+ "\n",
+ "$$\n",
+ "\\begin{equation}\n",
+ " \\tag{IVP}\n",
+ " \\dot{x}(t) = f(t, x(t)), \\quad x(t_0) = x_0,\n",
+ " \\label{eq:ivp}\n",
+ "\\end{equation}\n",
+ "$$\n",
+ "\n",
+ "with $f : \\Omega \\in \\mathrm{R} \\times \\mathrm{R}^n \\to \\mathrm{R}^n$, \n",
+ "$\\Omega$ an open set and $(t_0, x_0) \\in \\Omega$. Let us assume that $f$ is **continuous**.\n",
+ "\n",
+ "**_Definition._** We call a solution of $\\eqref{eq:ivp}$ any pair $(I, x)$ such that $I$ is an open interval of $\\mathrm{R}$ containing $t_0$, $x : I \\to \\mathrm{R}^n$ is a differentiable mapping on $I$ and such that:\n",
+ "\n",
+ "* $(t, x(t)) \\in \\Omega$, $\\forall t \\in I$,\n",
+ "* $\\dot{x}(t) = f(t, x(t))$, $\\forall t \\in I$,\n",
+ "* $x(t_0) = x_0$.\n",
+ "\n",
+ "Such a solution is also called an *integral curve* of the differential equation $\\dot{x}(t) = f(t, x(t))$.\n",
+ "\n",
+ "**_Differential equation vs. integral equation._** The differential equation $\\dot{x}(t) = f(t, x(t))$ with the initial condition $x(t_0) = x_0$ is equivalent to the *integral equation* (see [the fundamental theorem of calculus](https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus))\n",
+ "\n",
+ "$$\n",
+ " x(t) = x_0 + \\int_0^s f(s, x(s)) ~\\mathrm{d}s.\n",
+ "$$\n",
+ "\n",
+ "**_Remark._** If $f$ is continuous (resp. $C^k$) and $(I, x)$ is a solution, then $x$ is $C^1$ (resp. $C^{k+1})$ on $I$.\n",
+ "\n",
+ "<div class=\"alert alert-warning\">\n",
+ "\n",
+ "**Goal**\n",
+ "\n",
+ "Compute a numerical approximation of a solution $(I, x)$.\n",
+ " \n",
+ "</div>\n",
+ "\n",
+ "We consider a partition $t_0 < t_1 < ... < t_N = t_f$, $[t_0, t_f] \\in I$. Let $h_i := t_{i+1}-t_i$ denote the time steps (not necessarily equal) for $i = 0, N-1$ and $h_\\mathrm{max} = \\max_i(h_i)$ the longest step.\n",
+ "The goal is to compute iteratively approximations of $x(t_1)$, ..., $x(t_N)$ that we will denote by $x_1$, ..., $x_N$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Preliminaries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Parameters for integration\n",
+ "Nsteps = 10 # Number of integration steps"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Euler"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The [Euler scheme](https://en.wikipedia.org/wiki/Euler_method) is simply given by the following approximation of the integral:\n",
+ "\n",
+ "$$\n",
+ " \\int_{t_i}^{t_{i+1}} f(s, x(s)) ~\\mathrm{d}s \\approx h_i f(t_i, x_i).\n",
+ "$$\n",
+ "\n",
+ "Hence the Euler scheme is given by\n",
+ "\n",
+ "$$\n",
+ " x_{i+1} = x_i + h_i f(t_i, x_i).\n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 1:_**\n",
+ " \n",
+ "Complete the code of **ode_euler** (see the documentation of the function for details).\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " ||(cos(t), -sin(t)) - x|| = [0.05055979 0.00108516] \t t = 3.141592653589793\n"
+ ]
+ }
+ ],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 1 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# Euler integrator\n",
+ "#\n",
+ "def ode_euler(f, t0, x0, tf, N):\n",
+ " \"\"\"\n",
+ " Computes the approximated solution at time tf of \n",
+ "\n",
+ " dx = f(t, x), x(t0) = x0\n",
+ " \n",
+ " with the Euler scheme and uniform step size.\n",
+ " \n",
+ " Inputs: \n",
+ " \n",
+ " - f : dynamics\n",
+ " - t0 : initial time, float\n",
+ " - x0 : initial condition, array\n",
+ " - tf : final time, float\n",
+ " - N : number of steps, integer\n",
+ " \n",
+ " Outputs:\n",
+ " \n",
+ " - x : the solution x(tf) \n",
+ " \"\"\"\n",
+ " \n",
+ " tspan = np.linspace(t0, tf, N+1)\n",
+ " h = (tf-t0)/N\n",
+ " x = x0\n",
+ " \n",
+ " for t in tspan[1:]:\n",
+ " x = x + h*f(t, x)\n",
+ " \n",
+ " return x\n",
+ "\n",
+ "# Test of the Euler integrator\n",
+ "# We have x(t) = (cos(t), -sin(t))\n",
+ "t = np.pi\n",
+ "x = ode_euler(lambda t, x: np.array([x[1], -x[0]]), 0.0, np.array([1.0, 0.0]), t, 100)\n",
+ "print(' ||(cos(t), -sin(t)) - x|| = ', np.array([np.cos(t), -np.sin(t)])-x, \\\n",
+ " '\\t t = ', t)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 2:_**\n",
+ " \n",
+ "Complete the code of **hvfun** implementing the Hamiltonian system.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 2 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# Hamiltonian system\n",
+ "#\n",
+ "def hvfun(t, z):\n",
+ " n = dimx\n",
+ " x = z[0:n]\n",
+ " p = z[n:2*n]\n",
+ "# hv = 0.0\n",
+ " hv = np.array([x[1], -mu*x[1]**2+p[1], 0.0, -(p[0]-2.0*mu*x[1]*p[1])])\n",
+ " return hv"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 3:_**\n",
+ " \n",
+ "Complete the code of **shoot_euler** implementing the shooting function using **ode_euler** for integration.\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 3 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# Shooting function with Euler method\n",
+ "#\n",
+ "def shoot_euler(p0):\n",
+ " n = dimx\n",
+ " z0 = np.hstack((x0, p0))\n",
+ " zf = ode_euler(hvfun, t0, z0, tf, Nsteps)\n",
+ " xf = zf[0:n]\n",
+ " s = xf - xf_target\n",
+ " return s"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 1.967806967940155e+00 1.414213562373095e-01\n",
+ " 2 7.763352078391242e-01 1.925483764232603e+01\n",
+ " 3 8.714030918936800e-01 3.049871913351400e+01\n",
+ " 4 5.872090745406082e-01 3.560501399402753e+01\n",
+ " 5 2.014006521293087e-01 3.231327643632874e+01\n",
+ " 6 1.931710384142391e-03 3.316264831206244e+01\n",
+ " 7 8.043024319278244e-05 3.317049712945209e+01\n",
+ " 8 1.579715263727760e-06 3.317019011559066e+01\n",
+ " 9 3.292283942567928e-09 3.317019601604508e+01\n",
+ " 10 1.643167583551767e-13 3.317019600377284e+01\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [30.73610989 12.47210694]\n",
+ " f(xsol) = [-1.70974346e-14 -1.63424829e-13]\n",
+ " nfev = 10\n",
+ " njev = 1\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ " p0_euler = [30.73610989 12.47210694] \n",
+ " ||p0_euler-p0_nutopy|| = 1.2572301914908524 \n",
+ " shoot(p0_euler) = [-0.16689276 -0.36186443]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Resolution of the shooting function\n",
+ "p0_guess = np.array([0.1, 0.1])\n",
+ "sol_euler = nt.nle.solve(shoot_euler, p0_guess); p0_euler = sol_euler.x\n",
+ "\n",
+ "# we compare the solution with the one obtained with nutopy\n",
+ "# we call the shooting function from nutopy\n",
+ "print(' p0_euler =', p0_euler, \\\n",
+ " '\\n ||p0_euler-p0_nutopy|| =', np.linalg.norm(p0_euler-p0_nutopy), \\\n",
+ " '\\n shoot(p0_euler) =', shoot(p0_euler))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 4 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot solution\n",
+ "plotSolution(p0_euler)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Runge"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can show that the global error $||x_N - x(t_f)||$ behaves like $Ch_\\mathrm{max}$, where $C$ is a constant depending on the problem and $h_\\mathrm{max}$ is the maximal step size. Hence, if we want a precision of 6 decimals for instance, then, one would need about a million steps, which is not very satisfactory. The obvious idea to improve the numerical accuracy is to approximate the integral by a quadrature formulae of higher order. If we exploit the middle point, we have\n",
+ "\n",
+ "$$\n",
+ " x(t_{i+1}) \\approx x_i + h_i f(t_i + \\frac{h_i}{2}, x(t_i + \\frac{h_i}{2})).\n",
+ "$$\n",
+ "\n",
+ "The problem here is that we do not know the value of $x(t_i + \\frac{h_i}{2})$. At this stage, the idea is to approximate it by an Euler step: $x(t_i + \\frac{h_i}{2}) \\approx x_i + \\frac{h_i}{2} f(t_i, x_i)$. At the end, we obtain what we call the [Runge scheme](https://en.wikipedia.org/wiki/Midpoint_method) (or midpoint method):\n",
+ "\n",
+ "$$\n",
+ " x_{i+1} = x_i + h_i f(t_i + \\frac{h_i}{2}, x_i + \\frac{h_i}{2} f(t_i, x_i)).\n",
+ "$$\n",
+ "\n",
+ "Using the Runge, we can show that the global error is bounded by $Ch_\\mathrm{max}^2$. Hence, to obtain a precision of 6 digits, a thousands steps will usually do."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 4:_**\n",
+ " \n",
+ "Complete the code of **ode_runge** (see the documentation of the function for details).\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " ||(cos(t), -sin(t)) - x|| = [ 1.20427602e-05 -5.16624482e-04] \t t = 3.141592653589793\n"
+ ]
+ }
+ ],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 4 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# Runge integrator\n",
+ "#\n",
+ "def ode_runge(f, t0, x0, tf, N):\n",
+ " \"\"\"\n",
+ " Computes the approximated solution at time tf of \n",
+ "\n",
+ " dx = f(t, x), x(t0) = x0\n",
+ " \n",
+ " with the Runge scheme and uniform step size.\n",
+ " \n",
+ " Inputs: \n",
+ " \n",
+ " - f : dynamics\n",
+ " - t0 : initial time, float\n",
+ " - x0 : initial condition, array\n",
+ " - tf : final time, float\n",
+ " - N : number of steps, integer\n",
+ " \n",
+ " Outputs:\n",
+ " \n",
+ " - x : the solution x(tf) \n",
+ " \"\"\"\n",
+ " tspan = np.linspace(t0, tf, N+1)\n",
+ " h = (tf-t0)/N\n",
+ " x = x0\n",
+ " for t in tspan[1:]:\n",
+ " k1 = f(t, x)\n",
+ " k2 = f(t+h/2, x+(h/2)*k1)\n",
+ " x = x + h*k2\n",
+ " return x\n",
+ "\n",
+ "# Test of the Runge integrator\n",
+ "# We have x(t) = (cos(t), -sin(t))\n",
+ "t = np.pi\n",
+ "x = ode_runge(lambda t, x: np.array([x[1], -x[0]]), 0.0, np.array([1.0, 0.0]), t, 100)\n",
+ "print(' ||(cos(t), -sin(t)) - x|| = ', np.array([np.cos(t), -np.sin(t)])-x, \\\n",
+ " '\\t t = ', t)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Shooting function with Runge method\n",
+ "def shoot_runge(p0):\n",
+ " n = dimx\n",
+ " z0 = np.hstack((x0, p0))\n",
+ " zf = ode_runge(hvfun, t0, z0, tf, Nsteps)\n",
+ " xf = zf[0:n]\n",
+ " s = xf - xf_target\n",
+ " return s"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 1.967134895295981e+00 1.414213562373095e-01\n",
+ " 2 1.767925240530967e+00 1.799940022905573e+01\n",
+ " 3 1.259960259144468e+00 3.478958349066952e+01\n",
+ " 4 1.729469341852931e+00 3.830379709452797e+01\n",
+ " 5 7.454299618763681e-01 3.575955343995667e+01\n",
+ " 6 4.995424447550748e-01 3.510337739286172e+01\n",
+ " 7 1.863642739895163e-02 3.381938420706238e+01\n",
+ " 8 2.220983908854785e-03 3.387938502752595e+01\n",
+ " 9 4.633520849820257e-04 3.388375606015803e+01\n",
+ " 10 3.201130105575809e-05 3.388288851655970e+01\n",
+ " 11 3.067154905436612e-08 3.388282399525519e+01\n",
+ " 12 2.467268656218346e-10 3.388282393446912e+01\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [31.39989788 12.73154235]\n",
+ " f(xsol) = [5.20279375e-11 2.41178855e-10]\n",
+ " nfev = 12\n",
+ " njev = 1\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ " p0_runge = [31.39989788 12.73154235] \n",
+ " ||p0_runge-p0_nutopy|| = 0.5451475363343861 \n",
+ " shoot(p0_runge) = [-0.09338002 -0.22667258]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Resolution of the shooting function\n",
+ "p0_guess = np.array([0.1, 0.1])\n",
+ "sol_runge = nt.nle.solve(shoot_runge, p0_guess); p0_runge = sol_runge.x\n",
+ "\n",
+ "# we compare the solution with the one obtained with nutopy\n",
+ "# we call the shooting function from nutopy\n",
+ "print(' p0_runge =', p0_runge, \\\n",
+ " '\\n ||p0_runge-p0_nutopy|| =', np.linalg.norm(p0_runge-p0_nutopy), \\\n",
+ " '\\n shoot(p0_runge) =', shoot(p0_runge))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 4 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot solution\n",
+ "plotSolution(p0_runge)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Rk4"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The Euler method is a order 1 method while the Runge method is of order 2. A method of order $p$ has a global error bounded by $Ch_\\mathrm{max}^p$. To improve the numerical accuracy we can continue and define new methods of higher orders. The main method of order 3 is given by the [Heun scheme](https://en.wikipedia.org/wiki/Heun%27s_method). In this part, we will implement a method of order 4 simply called *rk4 method*. The Euler, Runge, Heun and rk4 methods are parts of what we call explicit [Runge-Kutta](https://en.wikipedia.org/wiki/Runge–Kutta_methods) methods.\n",
+ "\n",
+ "**_Remark_.** In the following definition, we give only the first iteration: $x_1 = x_0 + h \\Phi(t_0, x_0, h)$.\n",
+ "\n",
+ "**_Definition._** Let $s$ be an integer (the number of *stages*). \n",
+ "We call a *s-stages explicit Runge-Kutta* method for (IVP), a method defined by the scheme\n",
+ "\n",
+ "$$\n",
+ "\\begin{equation}\\label{eq:Runge-Kutta}\n",
+ "\\begin{array}{l}\n",
+ "k_1=f(t_0,x_0)\\\\\n",
+ "k_2=f(t_0+c_2h,x_0+ha_{21}k_1)\\\\\n",
+ "\\vdots\\\\\n",
+ "k_s=f(t_0+c_sh,x_0+h\\sum_{i=1}^{s-1}a_{si}k_i)\\\\\n",
+ "x_1=x_0+h\\sum_{i=1}^{s}b_ik_i\n",
+ "\\end{array}\n",
+ "\\end{equation}\n",
+ "$$\n",
+ "\n",
+ "where the coefficients $c_i$, $a_{ij}$ and $b_i$ are constants.\n",
+ "\n",
+ "**_Assumptions._** We introduce $c_1=0$ and assume that $c_i=\\sum_{j=1}^{i-1}a_{ij}$ for $i=2,\\ldots,s$.\n",
+ "\n",
+ "A Runge-Kutta method is represented in practice by its *Butcher table*:\n",
+ "\n",
+ "$$\n",
+ "\\begin{array}{c|ccccc}\n",
+ "c_1 & & & & &\\\\\n",
+ "c_2 & a_{21} & & & & \\\\\n",
+ "c_3 & a_{31} & a_{32} & & &\\\\\n",
+ "\\vdots & \\vdots & \\vdots & \\ddots & & \\\\ \n",
+ "c_s & a_{s1} & a_{s2} & \\ldots & a_{ss-1} & \\\\ \\hline\n",
+ " & b_1 & b_2 & \\ldots & b_{s-1} & b_s\\\\\n",
+ "\\end{array}\n",
+ "$$\n",
+ "\n",
+ "We give the following Butcher tables:\n",
+ "\n",
+ "$$\n",
+ "\\begin{array}[t]{cccc}\n",
+ "\\begin{array}{c}\n",
+ "\\\\ \\\\ \\\\\n",
+ "\\begin{array}{c|c}\n",
+ "0 & \\\\\\hline\n",
+ "& 1\n",
+ "\\end{array}\n",
+ "\\end{array}\n",
+ "& \n",
+ "\\begin{array}{c}\n",
+ "\\\\ \\\\\n",
+ "\\begin{array}{c|cc}\n",
+ "0 & &\\\\\n",
+ "1/2 & 1/2 &\\\\ \\hline\n",
+ " & 0 & 1\n",
+ "\\end{array}\n",
+ "\\end{array}\n",
+ "&\n",
+ "\\begin{array}{c}\n",
+ "\\\\\n",
+ "& \\begin{array}{c|ccc}\n",
+ "0 & & & \\\\\n",
+ "1/3 & 1/3 & & \\\\\n",
+ "2/3 & 0 & 2/3 & \\\\ \\hline\n",
+ " & 1/4 & 0 & 3/4\n",
+ "\\end{array}\n",
+ "\\end{array}\n",
+ "& \n",
+ "\\begin{array}{c|cccc}\n",
+ "0 & & & &\\\\\n",
+ "1/2 & 1/2 & & &\\\\\n",
+ "1/2 & 0 & 1/2 & &\\\\ \n",
+ "1 & 0 & 0 & 1 &\\\\ \\hline\n",
+ " & 1/6 & 2/6 & 2/6 & 1/6\n",
+ "\\end{array} \\\\\n",
+ "\\textrm{Euler (order 1)} & \\textrm{Runge (order 2)} & \\textrm{Heun (order 3)} & \\textrm{rk4 method (order 4)}\n",
+ "\\end{array}\n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 5:_**\n",
+ " \n",
+ "Complete the code of **ode_rk4** (see the documentation of the function for details).\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " ||(cos(t), -sin(t)) - x|| = [-6.6754946e-10 2.5492652e-08] \t t = 3.141592653589793\n"
+ ]
+ }
+ ],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 5 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# RK4 integrator\n",
+ "#\n",
+ "def ode_rk4(f, t0, x0, tf, N):\n",
+ " \"\"\"\n",
+ " Computes the approximated solution at time tf of \n",
+ "\n",
+ " dx = f(t, x), x(t0) = x0\n",
+ " \n",
+ " with the rk4 scheme and uniform step size.\n",
+ " \n",
+ " Inputs: \n",
+ " \n",
+ " - f : dynamics\n",
+ " - t0 : initial time, float\n",
+ " - x0 : initial condition, array\n",
+ " - tf : final time, float\n",
+ " - N : number of steps, integer\n",
+ " \n",
+ " Outputs:\n",
+ " \n",
+ " - x : the solution x(tf) \n",
+ " \"\"\"\n",
+ " tspan = np.linspace(t0, tf, N+1)\n",
+ " h = (tf-t0)/N\n",
+ " x = x0\n",
+ " for t in tspan[1:]:\n",
+ " k1 = f(t, x)\n",
+ " k2 = f(t+h/2, x+(h/2)*k1)\n",
+ " k3 = f(t+h/2, x+(h/2)*k2)\n",
+ " k4 = f(t+h, x+h*k3)\n",
+ " x = x + (h/6)*(k1+2*k2+2*k3+k4)\n",
+ " return x\n",
+ "\n",
+ "# Test of the RK4 integrator\n",
+ "# We have x(t) = (cos(t), -sin(t))\n",
+ "t = np.pi\n",
+ "x = ode_rk4(lambda t, x: np.array([x[1], -x[0]]), 0.0, np.array([1.0, 0.0]), t, 100)\n",
+ "print(' ||(cos(t), -sin(t)) - x|| = ', np.array([np.cos(t), -np.sin(t)])-x, \\\n",
+ " '\\t t = ', t)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Shooting function with rk4 method\n",
+ "def shoot_rk4(p0):\n",
+ " n = dimx\n",
+ " z0 = np.hstack((x0, p0))\n",
+ " zf = ode_rk4(hvfun, t0, z0, tf, Nsteps)\n",
+ " xf = zf[0:n]\n",
+ " s = xf - xf_target\n",
+ " return s"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 1.967300774283730e+00 1.414213562373095e-01\n",
+ " 2 1.718121875205946e+00 1.798533569285286e+01\n",
+ " 3 1.406165562584493e+00 3.486476110144650e+01\n",
+ " 4 1.981046367008785e+00 3.935407562882144e+01\n",
+ " 5 7.222261105195386e-01 3.624812389853345e+01\n",
+ " 6 4.685797072830273e-01 3.555566002644467e+01\n",
+ " 7 3.156098318109074e-02 3.434490490616069e+01\n",
+ " 8 2.209657850974052e-03 3.442947696252523e+01\n",
+ " 9 6.854635293194169e-04 3.443344316235571e+01\n",
+ " 10 1.075121403765715e-04 3.443232650607474e+01\n",
+ " 11 2.196852996890357e-07 3.443211824931880e+01\n",
+ " 12 2.061014211109517e-09 3.443211782785873e+01\n",
+ " 13 1.899130372352069e-11 3.443211783182064e+01\n",
+ "\n",
+ " Results of the nle solver method:\n",
+ "\n",
+ " xsol = [31.8979059 12.96512003]\n",
+ " f(xsol) = [4.21995772e-12 1.85165216e-11]\n",
+ " nfev = 13\n",
+ " njev = 1\n",
+ " status = 1\n",
+ " success = True \n",
+ "\n",
+ " Successfully completed: relative error between two consecutive iterates is at most TolX.\n",
+ "\n",
+ " p0_rk4 = [31.8979059 12.96512003] \n",
+ " ||p0_rk4-p0_nutopy|| = 0.005271636844688571 \n",
+ " shoot(p0_rk4) = [0.00280851 0.00846786]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Resolution of the shooting function\n",
+ "p0_guess = np.array([0.1, 0.1])\n",
+ "sol_rk4 = nt.nle.solve(shoot_rk4, p0_guess); p0_rk4 = sol_rk4.x\n",
+ "\n",
+ "# we compare the solution with the one obtained with nutopy\n",
+ "# we call the shooting function from nutopy\n",
+ "print(' p0_rk4 =', p0_rk4, \\\n",
+ " '\\n ||p0_rk4-p0_nutopy|| =', np.linalg.norm(p0_rk4-p0_nutopy), \\\n",
+ " '\\n shoot(p0_rk4) =', shoot(p0_rk4))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 4 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot solution\n",
+ "plotSolution(p0_rk4)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Step 3: Replacing the Newton solver"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this part, we define a Newton method to solve the shooting equations. In the description of the shooting equations, we use the rk4 integrator to compute the flow of the Hamiltonian system."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Preliminaries\n",
+ "\n",
+ "The following methods may be used to print information during the interations of the Newton solver."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def static_vars(**kwargs):\n",
+ " def decorate(func):\n",
+ " for k in kwargs:\n",
+ " setattr(func, k, kwargs[k])\n",
+ " return func\n",
+ " return decorate\n",
+ "\n",
+ "@static_vars(counter=0)\n",
+ "def callbackPrint(x,f):\n",
+ " if(callbackPrint.counter==0):\n",
+ " print('\\n Calls |f(x)| |x|\\n ')\n",
+ " print('{0:10}'.format(callbackPrint.counter+1) + \\\n",
+ " '{0:23.15e}'.format(np.linalg.norm(f)) + \\\n",
+ " '{0:23.15e}'.format(np.linalg.norm(x)))\n",
+ " callbackPrint.counter += 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Coding the Newton solver"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us recall the [Newton method](https://en.wikipedia.org/wiki/Newton%27s_method). Let us consider the nonlinear system of equations\n",
+ "\n",
+ "$$\n",
+ " f(x) = 0_{\\mathrm{R}^n},\n",
+ "$$\n",
+ "\n",
+ "with $f : \\Omega \\subset \\mathrm{R}^n \\to \\mathrm{R}^n$, differentiable on the open set $\\Omega$. The Newton method consists in solving iteratively a linear approximation of the system of equations. Let $k$ be the current iteration and $x^{(k)}$ the current iterate. The linear approximation reads\n",
+ "\n",
+ "$$\n",
+ " f(x^{(k)} + d) = f(x^{(k)}) + J_f(x^{(k)}) d + o(||d||), \\quad d \\in \\mathrm{R}^n,\n",
+ "$$\n",
+ "\n",
+ "where $J_f$ is the Jacobian of $f$ and where we have used the [Landau notation](https://en.wikipedia.org/wiki/Big_O_notation). Let us set\n",
+ "\n",
+ "$$\n",
+ " f_k(d) = f(x^{(k)}) + J_f(x^{(k)}) d.\n",
+ "$$\n",
+ "\n",
+ "We update the iterate as follows:\n",
+ "$\n",
+ " x^{(k+1)} = x^{(k)} + d^{(k)},\n",
+ "$\n",
+ "where $d^{(k)}$ is the solution of \n",
+ "$\n",
+ " f_k(d) = 0.\n",
+ "$\n",
+ "\n",
+ "This system being linear, if $J_f(x^{(k)})$ is invertible, then the next iterate is given by\n",
+ "\n",
+ "$$\n",
+ " x^{(k+1)} = x^{(k)} - \\left( J_f(x^{(k)}) \\right)^{-1} f(x^{(k)}).\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"alert alert-info\">\n",
+ "\n",
+ "**_Question 6:_**\n",
+ " \n",
+ "Complete the code of **newton** (see the documentation of the function for details).\n",
+ " \n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ----------------------------\n",
+ "# Answer 6 to complete here\n",
+ "# ----------------------------\n",
+ "#\n",
+ "# Newton solver\n",
+ "#\n",
+ "def newton(f, jf, x0):\n",
+ " '''\n",
+ " Solve f(x) = 0, with a Newton method, starting from the iterate x0.\n",
+ " \n",
+ " Usage:\n",
+ " \n",
+ " x, y, flag, it = newton(f, jf, x0)\n",
+ " \n",
+ " Newton iteration:\n",
+ " \n",
+ " x_{k+1} = x_k - d_k, d_k solution of f'(x_k) d = - f(x_k)\n",
+ " \n",
+ " Inputs: \n",
+ " \n",
+ " - f : function f(x)\n",
+ " - jf : Jacobian of f\n",
+ " - x0 : initial iterate\n",
+ " \n",
+ " Returns:\n",
+ " \n",
+ " - x : solution of f(x)=0 if convergence, last iterate otherwise\n",
+ " - y : f(x)\n",
+ " - flag : -1 if itermax is reached,\n",
+ " 1 if ||d|| < tolx * max(||x||, 1) at the last iterate\n",
+ " - it : number of iterations\n",
+ " \n",
+ " Numpy use:\n",
+ " \n",
+ " - linear.solve to solve Ax=b.\n",
+ " - linalg.norm to compute the norm of a vector\n",
+ " - maximum\n",
+ " \n",
+ " Remark: you can use callbackPrint to plot infos during the iterations.\n",
+ " Do not forget to reset the counter: callbackPrint.counter=0 before return.\n",
+ " \n",
+ " '''\n",
+ " tolx = 1e-6\n",
+ " itermax = 50\n",
+ " \n",
+ " i = 0\n",
+ " x = x0\n",
+ " flag = 0\n",
+ " \n",
+ " while flag == 0:\n",
+ " \n",
+ " # get f(x) and Jf(x)\n",
+ " A = jf(x)\n",
+ " b = f(x)\n",
+ " \n",
+ " # print\n",
+ " callbackPrint(x, b)\n",
+ " \n",
+ " # solve the linear system\n",
+ " d = np.linalg.solve(A, b)\n",
+ " \n",
+ " # update the iterate\n",
+ " x = x - d\n",
+ " \n",
+ " # test stop criterion\n",
+ " i = i + 1\n",
+ " if(i==itermax):\n",
+ " flag = -1\n",
+ " elif(np.linalg.norm(d)<tolx*np.maximum(np.linalg.norm(x), 1.0)):\n",
+ " flag = 1 \n",
+ " \n",
+ " # print\n",
+ " b = f(x)\n",
+ " callbackPrint(x, b)\n",
+ " \n",
+ " # reset counter\n",
+ " callbackPrint.counter=0\n",
+ " \n",
+ " # return\n",
+ " return x, b, flag, i"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 1.000000000000000e+00 1.414213562373095e+00\n",
+ " 2 5.337630192336734e-01 1.734119814433538e+00\n",
+ " 3 6.588879577933728e-02 1.572058663656674e+00\n",
+ " 4 9.572191917890302e-05 1.570796329712061e+00\n",
+ " 5 2.923566265536036e-13 1.570796326794897e+00\n",
+ " 6 6.123233995736766e-17 1.570796326794897e+00\n",
+ "(array([1.57079633, 0. ]), array([6.123234e-17, 0.000000e+00]), 1, 5)\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Test on the functions cosinus and sinus\n",
+ "print(newton(lambda x: np.array([np.cos(x[0]), np.sin(x[1])]), \\\n",
+ " lambda x: np.array([[-np.sin(x[0]), 0], [0, np.cos(x[1])]]), \\\n",
+ " np.array([1.0, 1.0])))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Solve the shooting equations"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Jacobian of the shooting function\n",
+ "def jshoot(p0):\n",
+ " \"\"\"jac = jshoot(p0)\n",
+ "\n",
+ " Jacobian of shooting function wrt. p0\n",
+ " \"\"\"\n",
+ " n = dimx\n",
+ " dp0 = np.eye(n)\n",
+ " jac = np.zeros((n, n))\n",
+ "\n",
+ " for i in range(0, n):\n",
+ " _, jac[:, i] = shoot((p0, dp0[i, :]))\n",
+ "\n",
+ " return jac"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Calls |f(x)| |x|\n",
+ " \n",
+ " 1 1.967300774283730e+00 1.414213562373095e-01\n",
+ " 2 7.385204030659501e+00 2.683757631301588e+01\n",
+ " 3 3.301727242107068e+00 2.067764703459671e+01\n",
+ " 4 5.124424337033568e-01 3.243074079406659e+01\n",
+ " 5 1.072191710682703e-02 3.438919455778397e+01\n",
+ " 6 9.531293521908929e-06 3.443203660979187e+01\n",
+ " 7 9.649733708236964e-08 3.443211793181983e+01\n",
+ " 8 1.438328245247572e-10 3.443211783256179e+01\n",
+ "\n",
+ " p0_sol = [31.89790591 12.96512003] \n",
+ " shoot = [0.00280851 0.00846786] \n",
+ " flag = 1 \n",
+ " iterations = 7\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Resolution of the shooting function\n",
+ "p0_guess = np.array([0.1, 0.1])\n",
+ "p0_sol, S_sol, flag, it = newton(shoot_rk4, jshoot, p0_guess)\n",
+ "print('\\n p0_sol =', p0_sol, \\\n",
+ " '\\n shoot =', shoot(p0_sol), \\\n",
+ " '\\n flag =', flag, \\\n",
+ " '\\n iterations =', it)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 900x600 with 4 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot solution\n",
+ "plotSolution(p0_sol)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}