Can I solve equations backward in time? (Pontryagin maximum principle optimal control problem)

Hello. I am trying to solve a problem with 7 states in the time interval (0,T), using Pontryagin Maximum Principle. I already have state, costate and optimal input equations, but it is quite hard to obtain its analytical equations since its nonlinear differential equation set with 15 variables. So I have modeled in Simulink. But the problem is, adjoint equations' solving method is, considering the problem backwards in time: starting from time T, up to 0. And I dont know a way to implement it on Matlab (Simulink, or in a toolbox). If anybody in the know could help me with the problem, I would be grateful.

[muhammad naeem]

Hi have you solved the problem

[Praveen Kumar]

Hi,

Have you solved the problem? I am also working on similar problem but with less states, but I have succussefully solved backward in ODE solver. The code is less efficient and its difficult to find initial step, control and costate.

[Gamze Balkan]

Hi, I have simplify the system and recuded it to 3 states, but analytical solution was still impossible to obtain, and I have put the problem aside for a while unfortunately. How many states do you have? Do you suggest ODE solver rather than Simulink?

[Praveen Kumar]

Only one state. Even though ODE is working, its very slow and results seems inaccurate sometimes. There is no way to prove the results are optimal.

[Siddhartha Ganguly]

Hi @Praveen Kumar can you please elaborate how did you solved it? it is possible to share your code (work) ?

[Praveen Kumar]

Hi Siddhartha,

Please check the following methods (codes) to solve such problems. I have used "eg2OC_descent" method for my problem.

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

Answer 1

[Torsten]

All MATLAB ODE-solvers can integrate backward in time. Just specify "tspan=[T 0]".

Best wishes

Torsten.

[Gamze Balkan]

Thank you for the answer! But I think my problem cannot be solved with ode since it has more than one independent variable in the dif. equation, what do you think? Even so, where can I make these setting and run it in Simulink, not in an mfile?

[yarik stepan]

Can you share the problem statement?

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