N-step off-line MPC design of nonhomogeneous Markov jump systems: A suboptimal case

Abstract

This paper mainly concerns N-step off-line suboptimal predictive controller design for discrete nonhomogeneous Markov jump systems, in which the Markov chains are time-varying transition probabilities matrix modeled as a polytope. The design procedure is divided into N-step, more precisely, the first is to design the Nth step when the changes of Euclidean form of mode-dependent feedback law between the Nth and the (N+1)th asymptotically stable mode-dependent ellipsoids are less than the given accuracy. Then the Nth asymptotically stable mode-dependent invariant ellipsoid is defined. In the previous (N−1) steps, an off-line mode-dependent predictive controller is designed to drive the state to this small area including the origin. Compared with on-line MPC algorithm, the computation time is dramatically reduced while the dynamic performance of controller is comparable. One numerical example is presented to illustrate the validity of the developed results.