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

This paper mainly concerns N-step off-line suboptitnal predictive controller design for discrete nonhotnogeneous Markov jump systems, in which the Markov chains are titne-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 algorithtn, the computation time is dramatically reduced while the dynamic performance of controller is comparable. One nutnerical example is presented to illustrate the validity of the developed results. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.