Minimization of cost function on MPC

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Chandrakanth Pavanaskar
回答： Sam Chak 2022-11-7
Hello,
I want to optimize a cost function of MPC which is output reference tracking as shown below:
min J(∆u) = ||xref(k + i) − x(k + i)||2 Q+ ||∆u(k + i)||2 R + ||xref(k + N) − x(k + N)||2 S, where Q,R and S are weight matrices.
Can anyone tell me how can I optimize this with constraint -1<∆u<1. Is it better use solver or can I optimize it without using solver?
If using solver, how can I convert into standard solver form?
If without using solver, which function to be used to minimize this cost function?
Any help is appreciated. Thanks in advance
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Sam Chak
Sam Chak 2022-11-6
Hi @Chandrakanth Pavanaskar
I think it depend on the problem and how you want to call quadprog() to perform the minimization and update the desired parameter in each iteration. If it is a MPC problem, then I prefer to use mpc() command:
mpcobj = mpc(plant, ts, P, M, W, MV, OV, DV)
https://www.mathworks.com/help/mpc/ref/mpc.html
Chandrakanth Pavanaskar
Chandrakanth Pavanaskar 2022-11-6
Hi @Sam Chak,
I have not used mpc command or toolbox in my optimization proble. I created matrices which predicts future states and optimize the control variable. I just wanted to know how can I give initial state as 0 and update the state for each iteration as my control variable and state changes every iteration and without using mpc commands.
Thank you

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Sam Chak
Sam Chak 2022-11-7
Hi @Chandrakanth Pavanaskar
You have a system model sys and I presume that you have written your own code for the ODE_solver to run the sys.
Under normal circumstances, you should be able to specify the initial states y0 in the ODE_solver.
The solver should produce the numerical solution array y that corresponds to a value returned in time vector t.
With the data, you can run your own optim_solver to produce some control action u.
Then, update the initial states y0 with final value of the states y(end) from the last iteration.
Finally, repeat the loop/steps by running the ODE_solver > the optim_solver until the specified number of iteration is completed.

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