From 47e579fcca722211015d4b6b19f2b318e860c56d Mon Sep 17 00:00:00 2001 From: Olivier Cots <61-ocots@users.noreply.022e47118ec0> Date: Fri, 26 Mar 2021 10:51:59 +0000 Subject: [PATCH] Update lecture1.md --- course/lecture/lecture1.md | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) diff --git a/course/lecture/lecture1.md b/course/lecture/lecture1.md index 88a7338..1cf2153 100644 --- a/course/lecture/lecture1.md +++ b/course/lecture/lecture1.md @@ -5,6 +5,10 @@ ------ +[Part II](lecture2.md) + +------ + **_Abstract_** 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). @@ -18,7 +22,7 @@ The goal of this presentation is that at the end, you will be able to implement **_Contents_** [[_TOC_]] - + ## I) Statement of the optimal control problem and necessary conditions of optimality ### a) Definition of the optimal control problem @@ -300,3 +304,9 @@ Computing we get, ```math u(t) = p(t) = (0, \frac{1}{t_f}), \quad \lambda = \frac{1}{t_f}, \quad x(t) = (t, \frac{t}{t_f}). ``` + +------ + +[Part II](lecture2.md) + +------ -- GitLab