Constrained linear system under disturbance feedback: Convergence with probability one

This paper considers a control parametrization under Model Predictive Control framework for constrained linear discrete time systems with bounded additive disturbances. Like the control parametrization in recent literature, the proposed parametrization uses affine disturbance feedback but includes an additional term. As a result, the parametrization has the same representative ability but has a different closed-loop convergence property. More exactly, the state of the closed-loop system converges to the minimal invariant set with probability one. Deterministic convergence to the same set is also possible if a less intuitive cost function is utilized. Numerical experiments are provided that validate the results.