When determining the present control move u(k) using an MPC problem, a numerical control problem is solved online. This is due to the presence of input/state/output constraints, which prevent the use of simple control laws (such as the u=Kx obtained for LQR offline) even for linear systems.

Different formulations of MPC require a different solver, depending on the cost function (typically, quadratic or linear), on the equality constraints imposed by the system dynamics (linear or nonlinear), and on the imposed constraints (mostly, polyhedral). In the MPC toolbox for Matlab, in the basic formulation, the problem is based on a linear (or linearized) state-space model (A,B,C,D) of the system, using a quadratic cost function and linear inequality constraints on inputs and states. As a result, a quadratic program (QP) is solved, typically employing an active-set solver.

For more information, please refer to the online documentation: 

http://www.mathworks.com/help/mpc/model-predictive-control-basics.html

Hope it helps!

Matteo

MPC is a optimal control problem. MATLAB toolbox takes your MPC model and re-writes it in the form of cost functions and so on.

And thus the most commonly algorithm used for MPC solving is LQR. 

A short comprehensive description can be found following the link. 

http://dsp.vscht.cz/konference_matlab/MATLAB09/prispevky/099_skrabanek.pdf

Hope this helps.

Regards,

Mushfiqul Alam

When determining the present control move u(k) using an MPC problem, a numerical control problem is solved online. This is due to the presence of input/state/output constraints, which prevent the use of simple control laws (such as the u=Kx obtained for LQR offline) even for linear systems.

Different formulations of MPC require a different solver, depending on the cost function (typically, quadratic or linear), on the equality constraints imposed by the system dynamics (linear or nonlinear), and on the imposed constraints (mostly, polyhedral). In the MPC toolbox for Matlab, in the basic formulation, the problem is based on a linear (or linearized) state-space model (A,B,C,D) of the system, using a quadratic cost function and linear inequality constraints on inputs and states. As a result, a quadratic program (QP) is solved, typically employing an active-set solver.

For more information, please refer to the online documentation: 

http://www.mathworks.com/help/mpc/model-predictive-control-basics.html

Hope it helps!

Matteo

It is the Linear MPC which is used with a linear model of your system or the linearized model also and then a quadratic problem is solved to fid the optimal control low.

Thank you everyone for your generous answers!