On switched MPC of a class of switched linear systems with modal dwell time

Lixian Zhang, Richard D. Braatz

Abstract: This article investigates the model predictive control (MPC) of a class of discrete-time switched linear systems with modal dwell time (MDT). In contrast with existing hybrid MPC theories, where the state-dependent switching can capture the mode variations during the prediction horizon, this article considers switching instants to be unknown a priori. The prediction model is limited to be the currently activated subsystem, which facilitates the MPC design associated individually to each subsystem. Consequently, by the invariance of the reachable sets of the feasible region of each subsystem, the minimal admissible MDT is determined so as to guarantee both the persistent feasibility of MPC design and system stability. The conservatism of ignoring the position of the states at the switching instants is further reduced by allowing for the minimal admissible MDT to be state-dependent. It is shown that the system stability is guaranteed as long as the persistent feasibility is ensured both within the subsystems and at the switching instants. Finally, when the MDT is given, an algorithm is developed for determining the feasible region for the switched systems.