QP formulation from the MPC toolbox

Hi,

I am studying different QP solvers (e.g. qpOASES, OSQP, DAQP and Gurobi) for a project I am doing at my university. I want to test their capabilites in MPC. I have tested them in the aircraft example and gotten some reasonable results, but now I wonder which QP formulation Matlab's mpc generates.

Does it create some sort of reduced-space condensed QP based on the state-space model? I am guessing this is the case because the hessian (H) of the objective function is only 11x11 for the MPC example mentioned above, with a horizon of 50 (4 states and 2 inputs).

I am guessing that it is not some sort of step-response model formulation (not for the aircraft model at least) because the model has unstable poles.

Does anyone have insights into this?

Thanks

Answer 1

[Emmanouil Tzorakoleftherakis]

We are currently using the dense formula as you mentioned, but also working on adding support for sparse problems. The following two links may be helpful:

https://www.mathworks.com/help/mpc/ug/qp-solver.html

https://www.mathworks.com/help/mpc/ug/optimization-problem.html

[Elias Prytz]

This is exaclty what I was looking for, thank you!

[Muhammad]

Dear @Emmanouil Tzorakoleftherakis

I hope you're doing well. I have one confusion, I designed MPC controller using mpcobj and Simulink MPC Toolbox, I didn't put any constrainst to my MPC controller keeping all the values as default inf,-inf.. Its work well but now my professor asked me one question does your unconstrained MPC uses QP solver or not? If not then what kind of solver matlab/simulink is using for unconstrained mpc?

I checked with mpcobj.Optimizer (without constraint and with constraints its give me same response)

Algorithm: 'active-set'

ActiveSetOptions: [1×1 struct]

InteriorPointOptions: [1×1 struct]

MixedIntegerOptions: [1×1 struct]

MinOutputECR: 0

UseSuboptimalSolution: 0

CustomSolver: 0

CustomSolverCodeGen: 0

[Emmanouil Tzorakoleftherakis]

Hi,

I answered your question here.