Convergence properties of constrained linear system under MPC control law using affine disturbance feedback

This paper shows new convergence properties of constrained linear discrete time system with bounded disturbances under Model Predictive Control (MPC) law. The MPC control law is obtained using an affine disturbance feedback parametrization with an additional linear state feedback term. This parametrization has the same representative ability as some recent disturbance feedback parametrization, but its choice together with an appropriate cost function results in a different closed-loop convergence property. More exactly, the state of the closed-loop system converges to a minimal invariant set with probability one. Deterministic convergence to the same minimal invariant set is also possible if a less intuitive cost function is used. Numerical experiments are provided that validate the results.