A robust model predictive strategy for switched systems with unstabilizable modes and polytopic uncertainty

This investigation introduces a model predictive control approach for a specific type of switched system. The proposed method eliminates the need to assume the stabilizability of all modes and provides an online framework to ensure robust H∞performance in the presence of external disturbances. To achieve these goals, a simultaneous design of a persistent dwell time switching rule and a model predictive controller is accomplished by utilizing multiple Lyapunov functions to guarantee asymptotic stability. Furthermore, two types of cost functions are defined: one with a finite horizon for unstabilizable modes and another with an infinite horizon for stabilizable modes. To tackle feasibility challenges related to online optimization, a carefully chosen sequence of applying constraints corresponding to the Lyapunov stability conditions and cost functions is utilized to regulate the rate of energy variations in different modes. Consequently, this developed control approach expands the feasibility region and overcomes the conservative nature of schemes that depend on arbitrary switching laws and switched Lyapunov functions. Finally, a chemical system is employed to validate the proposed method, and its performance is thoroughly examined.