update readme

README.md

@@ -2,11 +2,21 @@
 
 # Geometric and numerical methods in optimal control II
 
+We present in this course 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).
+ We use the [nutopy package](https://ct.gitlabpages.inria.fr/nutopy/) to solve the optimal control problem by simple shooting.
+
+When the control law in feedback form is discontinuous, in the indirect context, we need to implement a **multiple** shooting method.
+ We will give a brief introduction to the multiple shooting method during the computer session on a simple example.
+
 ## Lecture
 
-[Lecture](https://ct.gitlabpages.inria.fr/gallery/shooting_tutorials/simple_shooting_general.html)
-([Notebook download link](course/lecture/simple_shooting_general.ipynb),
-[Notes](course/lecture/lecture.pdf))
+[Generalities about the indirect simple shooting method](https://ct.gitlabpages.inria.fr/gallery/shooting_tutorials/simple_shooting_general.html)
+
+[lecture notebook](course/lecture/simple_shooting_general.ipynb),
+[lecture notes](course/lecture/lecture.pdf)
 
 ## Exercices