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

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Praveen Kumar
Praveen Kumar on 13 Nov 2019
Commented: Praveen Kumar on 10 Aug 2020
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:
  1. Initialize states, co-state and control
  2. ODE45 solver in forward time to find states.
  3. ODE45 solver in backward time to find co-states
  4. Find hamiltonian and performance index. If difference between previous and present hamiltonian is below given threshold the stop iteration or else go to 5.
  5. Update the control with a selected step size.
I am facing many difficulties in implementation such as;
  1. Difficulty in selecting initial control and co-state.
  2. 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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