Question about fmincon including ODE

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Kenta
Kenta on 3 Sep 2014
Edited: Matt J on 3 Sep 2014
Dear all. I am using fmincon to optimize a constrained problem including integration of ODE. I want to ask a simple question about the applicability of fmincon: Can fmincon optimize the integration time as well as parameters? Or fmincon may be only applicable to time-fixed problems? For more information, I am putting the initial guess of integration time to fmincon, and intending to optimize integration time as well as other parameters. Regards, Kenta

Answers (2)

Matt J
Matt J on 3 Sep 2014
Edited: Matt J on 3 Sep 2014
Even when the integration time is not an unknown parameter, it is questionable whether fmincon is applicable. I assume your ODE is with constant coefficients and is higher than first order. In this case, the solution of the ODE is not a differentiable function of the unknown coefficients (or at least the characteristic roots are not). That doesn't rule out empirical success of course, i.e., you could just try it and hope the iterations don't stray into any bad regions.
But since you're already gambling with fmincon, there's no longer much reason to worry about rigour when you include integration time as an additional parameter. The objective as a function of integration time would have to be well-behaved, though. For example, if you are simply doing a least squares fit of the ODE solution to some given noisy data, I suspect that there might be lots of local minima as a function of the integration time, even when it is the only unknown parameter. Also, you would need appropriate constraints.Otherwise an integration time of zero should trivially give you the global minimum squared error.
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Kenta
Kenta on 3 Sep 2014
Edited: Matt J on 3 Sep 2014
Dear Matt J, thank you for your prompt reply. Indeed, the reason I worry about including integration time in fmincon as an additional parameter is that I found a similar subject in the following:
and Deepraj said 'fmincon' only provides solution to Constrained fixed time optimal system. But I couldn't find other documents about this issue, so I am puzzling.

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Alan Weiss
Alan Weiss on 3 Sep 2014
Take a look at this example. fmincon works just fine on the example, especially if you increase the DiffMinChange option a bit.
I think that you can use fmincon to optimize over integration time as well as other parameters.
Alan Weiss
MATLAB mathematical toolbox documentation

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