QP formulation from the MPC toolbox

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Elias Prytz
Elias Prytz 2023-10-20
评论： Emmanouil Tzorakoleftherakis 2024-5-29
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

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Emmanouil Tzorakoleftherakis
编辑：Emmanouil Tzorakoleftherakis 2023-10-23
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
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Muhammad
Muhammad 2024-5-29
编辑：Muhammad 2024-5-29
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

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