Algebraic Riccati Equation Solution for Code Generation

Hi all,

Knowing that the lqr, care and icare functions do not currently support code generation, does anyone have an alternative (code or function) that can be used for the computation of the state variable gain for a linear quadratic regulator?

In the past I have gone down the route of trying to solve the algebraic ricatti equation (ARE) using the Hamiltonian matrix (below is for the CARE, though can be altered for the DARE) to get the ARE solution using the schur function.

Whilst the schur decomposition supports code generation I also needed the ordschur function, which does not support code generation, to reorder the eigenvalues.

I actually can't remember if the ordschur is critical to the solution, so part of my question is do I even need to reorder the decomposition in order to appropriately solve the ARE, and if so if theres an alternative to ordschur that is support for code generation?

Z = [A -(B/R*B'); -Q -A'];
[U, S] = schur(Z);
[U, S] = ordschur(U, S, 'lhp');
[m,n] = size(U);
U11 = U(1:(m/2), 1:(n/2));
U21 = U((m/2+1):m, 1:(n/2));
P = U21/U11;
K = inv(R)*B'*P

Thanks in advance!

Just some links for context:

https://uk.mathworks.com/help/referencelist.html?type=function&capability=codegen&listtype=alpha

https://uk.mathworks.com/help/matlab/ref/schur.html

https://uk.mathworks.com/help/matlab/ref/ordschur.html

https://en.wikipedia.org/wiki/Linear%E2%80%93quadratic_regulator

https://en.wikipedia.org/wiki/Algebraic_Riccati_equation

Answer 1

[Erivelton Gualter]

The solution of riccati equation using Simulink was answed here:

https://www.mathworks.com/matlabcentral/answers/87237-lqr-simulink-block-model by Gurkan KAVURAN.

It worked great for my application, which also evolves code generation. The solution is presented in the following link:

https://www.mathworks.com/matlabcentral/fileexchange/67268-simulink-block-of-lqr

I needed to change a line of code. Just check the comments of this file exchange page.

[Gary Zhang]

Thank you very much Erivelton. Your first link is working for real time code gen.

Answer 2

[Victory Friday]

Please did you finally find a way around it, I am having similar challenge.