Minimization of cost function on MPC

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Chandrakanth Pavanaskar
Chandrakanth Pavanaskar on 26 Oct 2022
Answered: Sam Chak on 7 Nov 2022
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
Chandrakanth Pavanaskar
Chandrakanth Pavanaskar on 6 Nov 2022
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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Answers (1)

Sam Chak
Sam Chak on 7 Nov 2022
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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