Solve Optimal Control problem with free-final-time using MATLAB?

Ehsan Ranjbari

2022 1 17

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I am trying to solve an Optimal Control problem that I have the initial state value (x0 = 0), but the x(tf) is free. The problem is as below: t = [0 31]

% function inside the integral (f),
f = (7*u)/100 - ((7*x)/1000 + 30)*((3*u)/500 + x + 1/200) + u^2/25
% state equation
Dx = (3*u)/500 + x + 1/200

I would love to know how can this kind of optimal problem can be solved?

I tried Pontryagin principle but the lack of boundary condition (x(tf)) caused an error.

Thanks in advance

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Torsten 2022-1-22

As I already said, my knowledge about optimal control problems is approximately 0.

What I understand is that you arrive at two ordinary differential equations - one for x, the other for p1 - , but that you only have one boundary condition (x(0)=0).

How do you want to fix a solution with only one boundary condition ?

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