EASY QUESTION ABOUT THE lsqlin COMMAND: Is it possible to use the lsqlin algorithm for MIMO systems (always with linear constraints)?

I have seen that lsqlin is usually used for SISO systems, but is it possible to use it also with MIMO systems always having linear constraints?

[Jon]

I'm not sure what you mean by SISO (single input single output) and MIMO (multiple input multiple output) systems in this context.

lsqlin finds the "best" solution to the equation Cx =d subject to linear constraints on the variable x. Are the elements of x each an "input" if so then there are certainly multiple inputs. Are the elements of the result Cx considered "output" if so there are multiple outputs. So would you consider this to be MIMO?

[DAMIANO]

Forgive me, I was inaccurate. I meant multiple variables x as inputs to get from Cx = d. Thank you

Answer 1

[Walter Roberson]

If you have two systems, A1, A2, B1, B2, and want to match A1*x1 = B1 and A2*x2 == B2 for independent sets x1 and x2, then you can generally do that in a single call by constructing blkdiag(A1,A2) and blkdiag(B1,B2) . This will not necessarily be any faster than doing the two separately and runs the risk that a singularity in one of them could spill over into computing the other one.

It is not necessary that the systems be completely independent -- but if they are not independent then blkdiag() by itself is not going to create the correct matrices.

[DAMIANO]

Thanks for your reply Mr Robertson. Yes, this also appears to me because if one has Reachability matrices whose inputs influence each other, the result of the quadratic cost of these (inputs) is not easy to discern. Mostly I introduced linear constraints on both inputs and states. Despite everything, to verify that the correct values ​​of the inputs were extracted from the inputs vector(I had 4 inputs - 2 completely indipendent inputs and 2 dipendent inputs - and 8 outputs: basically all the states of the system), I did some tests to control if the graphs were simulated correctly.

Answer 2

[Bruno Luong]

As long as you have a linear least-squares model, linear equality and inequality constraints then yes you can use lsqlin, as clearly stated by the doc page.