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course/lecture/lecture1.md

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+[Part II](lecture2.md)
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 **_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).
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 **_Contents_**
 
 [[_TOC_]]
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 ## I) Statement of the optimal control problem and necessary conditions of optimality
 
 ### a) Definition of the optimal control problem
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 ```math
     u(t) = p(t) = (0, \frac{1}{t_f}), \quad \lambda = \frac{1}{t_f}, \quad x(t) = (t, \frac{t}{t_f}).
 ```
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+------
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+[Part II](lecture2.md)
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+------