Any methods to solve optimal control indirect method such as Pontryagin Minimum Principle?

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Praveen Kumar 2019-11-13

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https://ww2.mathworks.cn/matlabcentral/answers/490833-any-methods-to-solve-optimal-control-indirect-method-such-as-pontryagin-minimum-principle

评论： Mohamed Abdullah 2023-3-19

PMP_EV.pdf

Hi,

I would like to solve an optimal control problem using Pontryagin Minimum Principle. There are few numerical techniques with MATLAB examples using sym toolbox, bvp4c and ODE45 using shooting method. I am trying to implement using ODE45 solver by following steps:

Initialize states, co-state and control
ODE45 solver in forward time to find states.
ODE45 solver in backward time to find co-states
Find hamiltonian and performance index. If difference between previous and present hamiltonian is below given threshold the stop iteration or else go to 5.
Update the control with a selected step size.

I am facing many difficulties in implementation such as;

Difficulty in selecting initial control and co-state.
The state is not bounded within a range as it must be. (must be between 0 and 1, and final state must be a desired value)

I have attached the reference paper which I am trying to implement. If anyone knows any MATLAB toolbox to solve the same, kindly let me know.

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Answer 1

M 2019-11-13

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编辑：M 2019-11-13

Hi,

here are some related questions to start with:

https://mathworks.com/matlabcentral/answers/440335-how-to-implement-optimal-control-using-pontryagin-s-minimum-principle-for-hess-in-ev-application-as

https://mathworks.com/matlabcentral/answers/438910-how-to-solve-in-matlab-2018b

https://mathworks.com/matlabcentral/answers/392949-can-i-solve-equations-backward-in-time-pontryagin-maximum-principle-optimal-control-problem

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Answer 2

Philipp Tiwald 2020-8-9

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https://ww2.mathworks.cn/matlabcentral/answers/490833-any-methods-to-solve-optimal-control-indirect-method-such-as-pontryagin-minimum-principle#answer_477163

Hi,

Im trying to implement a simular optimal controll problem. Could you share your solution?

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Praveen Kumar 2020-8-10

https://in.mathworks.com/matlabcentral/fileexchange/25889-an-optimal-control-tutorial-for-beginners

Try the above methods. These examples will help you to formulate the problem and use either of the solving method.

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Answer 3

Mohamed Abdullah 2023-3-17

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https://ww2.mathworks.cn/matlabcentral/answers/490833-any-methods-to-solve-optimal-control-indirect-method-such-as-pontryagin-minimum-principle#answer_1195340

Hello Praveen, do you mind sharing your Matlab code for the Problem you have attached in the PMP-EV file?

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Praveen Kumar 2023-3-18

I am sorry, the exact codes couldnt be shared as it is still under publication. Please find below sources for implementing the same.

Mohamed Abdullah 2023-3-19

Thank you very much. I have a question about the second link. I downloaded the zipped file but it appears to me that it contains only measured data not the algorithms itself.

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