Model Predictive Control Of Switched Systems

Switched systems are a class of hybrid dynamic systems that are pervasive in engineering applications. The switched system is widespread in the bio-engineering fields, aerospace and automotive industry. For the control problem of switched systems, it is generally assumed that the switching of the controllers is matched with that of the subsystems, i.e., they are activated synchronously at switching instant. In practical engineering, however, since it inevitably takes some time to identify the active subsystem and apply for the matched subsystems, which results in asynchronous switching. For complex constrained system, such as switched system, how to obtain the systemic method of designing controller to achieve the optimal performance, feasible control algorithm and the stabilization of the closed-loop system is a challenging problem of modern control theory.In this paper, the research on model predictive control is concerned for several switched systems. The main contributions are described as follows:1. The problem of a mixed H₂/H_∞ model predictive control（MPC） for a class of continuous-time switched singular systems with norm bounded disturbance is investigated. By using a switched Lyapunov function, sufficient conditions for the existence of MPC controller and switching strategy are obtained. In terms of linear matrix inequality, the designed state feedback controllers ensures that closed-loop systems satisfy high level of system performance measured by H₂ norm and a presented H_∞ disturbance attenuation level λ.2. This paper investigates the problem of asynchronously switched predictive control for a class of discrete-time systems with average dwell time（ADT）. The asynchronous switching means that the switchings instants of the candidate controllers lag behind those of the subsystems. By allowing the Lyapunov-like function to increase during the running time of active subsystems, the relationship between the maximal delay of asynchronous switching, the sampling time and the increase scale of the Lyapunov-like function is studied. Then, the extended stability results for switched systems with ADT in model predictive control（MPC） are derived. To solve a quasi-min-max optimal problem, the minimal ADT for admissible switching signals and the corresponding controller gains are designed to guarantee the closed-loop system to be globally uniformly exponentially stable（GUES）.