diff --git a/course/lecture/lecture1.md b/course/lecture/lecture1.md index 88a7338a5542c32c227842e7c2f19927734debe8..1cf21533f9f970420bba82fcc5bb7b7d72e82038 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) + +------