Reference tracking

[Matyjehouba]

Hello, I've been trying to use tinyMPC for reference tracking, but I am interested in tracking only one state, which seems impossible even with very large control horizon, so I've been going through the code and stumbled upon something I don't understand. In tiny_precompute_and_set_cache(...) there is a line of code initializing matrix Q1: tinyMatrix Q1 = Q + rho * tinyMatrix::Identity(nx, nx);

What I dont understand is why are you adding essentially two times the rho * Identity to the initial Q matrix. Why two times: because its called from the setup function where you already add the rho once.

Could I maybe use my original Q which is positive semidefinite for Pinf calculation and then at the end when saving Pinf add the rho*Identity? like this:
cache->Pinf = Pinf + rho * tinyMatrix::Identity(nx, nx);

[ishaanamahajan]

Hey @Matyjehouba , the first addition is needed for the ADMM augmented Lagrangian, and the second is done purely as a regularization choice. So yes, you can use the original Q since it will only remove the regularization, and does not change the optimization problem. However, at the end if you change Pinf, you might also want to change Kinf because those are all derived from the same LQR and should stay consistent.