How to specify a nonlinear mpc controller for continuous time delay differential equation state function?

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Kayvon
Kayvon 2023-3-14
评论： Kayvon 2023-3-20
I have a system of continuous-time nonlinear delay differential equations with two states and two explicit time delays. I would like to build a nonlinear mpc controller for this system, but I am not sure how to write a state function with time delays.
The system:
Where are the state varaibles, are constants, u is the manipulated variable, and are the continuous-time nonlinear state equations.
Is this possible to do using nlmpc ?

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Emmanouil Tzorakoleftherakis
You can basically add states to help model the delays. So your new discretized state vector would be [x(k) y(k) x(k-1) y(k-1) ... x(k-tau1/Ts) y(t-tau2/Ts)]. Then you can use the respective state function with nlmpc.
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Kayvon
Kayvon 2023-3-20
In this case I was able to rescale the time variable in the delay differential equations so that the needed time delays were small which made the computation tractable. But in other cases I like the idea of fitting a data-driven model and I'm going to look into that as well anyways.

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