Interpolation based Model Predictive Control Design for Markovian Jump Linear Systems

In this paper, an interpolation based model predictive control design is proposed for hard constrained Markovian jump linear systems with polytopic uncertainties. The adopted predictive control law is a linear combination of serval predetermined stabilizing feedback control laws. By performing the state decomposition, the domain of attraction of the predictive control law is proved to be the convex hull of each individual ones. The closed loop system is proved to evolve as an augmented high dimensional Markovian jump linear satem governed by the same transition probability matrix. An upper bound on the worst case infinite horizon expected objective function is obtained by solving LMIs, which serves as the objective function of the online MPC optimization. The resulting algorithm is proved to guarantee the satisfaction of the hard constrains and the mean square stability of the closed loop system. Finally, a numerical example is given to verify the efficiency of the proposed results.