Switched model predictive control of switched linear systems: Feasibility, stability and robustness

This paper is concerned with the issues of feasibility, stability and robustness on the switched model predictive control (MPC) of a class of discrete-time switched linear systems with mode-dependent dwell time (MDT). The concept of conventional MDT in the literature of switched systems is extended to the stage MDT of lengths that vary with the stages of the switching. By computing the steps over which all the reachable sets of a starting region are contained into a targeting region, the minimum admissible MDT is offline determined so as to guarantee the persistent feasibility of MPC design. Then, conditions stronger than the criteria for persistent feasibility are explored to ensure the asymptotic stability. A concept of the extended controllable set is further proposed, by which the complete feasible region for given constant MDT can be determined such that the switched MPC law can be persistently solved and the resulting closed-loop system is asymptotically stable. The techniques developed for nominal systems lay a foundation for the same issues on systems with bounded additive disturbance, and the switched tube-based MPC methodology is established. A required "switched" tube in the form of mode-dependent cross section is determined by computing a mode-dependent generalized robust positive invariant set for each error subsystem between nominal subsystem and disturbed subsystem. The theoretical results are testified via an illustrative example of a population ecological system.