MPC of a class of switched linear systems with ranged dwell-time constraints

This paper proposes a model predictive control (MPC) scheme for a class of switched linear systems under ranged dwell-time (RDT) constraints, capable of simultaneously optimizing the continuous control inputs as well as discrete switching sequences, with both recursive feasibility and asymptotic stability guarantees. The RDT admissible contractive set is proposed, and the equivalence between the asymptotic stability of the system and the existence of an RDT admissible contractive set is further demonstrated. Then, a novel MPC scheme is established by performing the following innovative techniques: (1) an embedded RDT admissible contractive set is characterized and computed as the terminal set, (2) the optimization problem in the MPC scheme is constructed with both continuous and discrete variables, which is further turned into a mixed-integer quadratic program (MIQP) problem for global optimization, (3) the recursive feasibility and stability are rigorously guaranteed under such a setting. Numerical examples are provided to illustrate the proposed method and verify its effectiveness.