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Commit edb69667 authored by Olivier Cots's avatar Olivier Cots
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Update lecture2.md

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...@@ -80,6 +80,8 @@ and we need a [Newton-like](https://en.wikipedia.org/wiki/Newton%27s_method) sol ...@@ -80,6 +80,8 @@ and we need a [Newton-like](https://en.wikipedia.org/wiki/Newton%27s_method) sol
**_Remark:_** **_Remark:_**
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. 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.
[Additional comments (video)](http://www.youtube.com/watch?v=YVG2Z_TEkBQ)
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<img src="../images/simple_shooting.png" width="400"> <img src="../images/simple_shooting.png" width="400">
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...@@ -98,8 +100,6 @@ Figure: Illustration of the shooting method in the cotangent space. The blue ext ...@@ -98,8 +100,6 @@ Figure: Illustration of the shooting method in the cotangent space. The blue ext
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[Additional comments (video)](http://www.youtube.com/watch?v=YVG2Z_TEkBQ)
### b) The iteration of the Newton solver and the Jacobian of the shooting function ### b) The iteration of the Newton solver and the Jacobian of the shooting function
[Additional comments (video)](http://www.youtube.com/watch?v=hVbi9kShR90) [Additional comments (video)](http://www.youtube.com/watch?v=hVbi9kShR90)
...@@ -110,4 +110,4 @@ Figure: Illustration of the shooting method in the cotangent space. The blue ext ...@@ -110,4 +110,4 @@ Figure: Illustration of the shooting method in the cotangent space. The blue ext
## IV) Numerical resolution of the shooting equations with the nutopy package ## IV) Numerical resolution of the shooting equations with the nutopy package
This part is there: [notebook lecture](lecture.ipynb). Please follow the procedure given [here](../../README.md) to install all packages and use `jupyter-lab` to execute the code and do the exercices. This part is there: [notebook lecture](lecture_simple_shooting.ipynb). Please follow the procedure given [here](../../README.md) to install all packages and use `jupyter-lab` to execute the code and do the exercices.
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