Probabilistic constrained stochastic model predictive control for Markovian jump linear systems with additive disturbance

Abstract

Abstract This paper is concerned with stochastic model predictive control for Markovian jump linear systems with additive disturbance, where the systems are subject to soft constraints on the system state and the disturbance sequence is finitely supported with joint cumulative distribution function given. By resorting to the maximal disturbance invariant set of the system, a model predictive control law is given based on a dynamic controller which is with guaranteed recursive feasibility and ensures the probabilistic constraints on the states. By optimizing the volume of the disturbance invariant set, the dynamic controller is given. The closed loop system under this control law is proven to be stable in the mean square sense. Finally, a numerical example is given to illustrate the developed results.