Optimal Control And Stability Of Switched Systems

Switched systems are an important class of hybrid systems, which consist of several subsystems (continuous-time subsystems or discrete-time subsystems or continuous-time and discrete-time subsystems) and a rule that orchestrates the switching among them. In the last four decades a study of switched systems has received much attention due to signaficance in theory and broad practical applications, and it is one of hotspot of research of control science at all times.In this dissertation we study optimal control, stability and estimates of the region of attraction of switched sytems. The main contributions are as follows.(1) In this dissertation we propose a new embedding approach to investigate the optimal control problem of the switched system with m modes. By means of the new embedding approach the switched systesm is embedded into a new larger family of systems and the corresponding optimal control problem is formulated for the new embedded system, and we directly use the Lyapunov theorem to prove the following key result: the set of trajectories of the switched system with m modes is dense in the set of trajectories of the embedded system. Based on the above key result we obtain optimal solutions and suboptimal solutions of the optimal control problem of the switched system with m modes by studying the embedded optimal control problem.(2)We study stability and stabilization of a new type of switched systems (switched systems with continuous-time and discrete-time subsystems) proposed in the literature. Up to now, for stability of such type of nonlinear switched systems there are not any available results. Therefore for a specific class of switched systems composed of continuous-time nonlinear subsystems and discrete-time uncertain subsystems we give an estimation of state of this class of switched systems, and from the estimation we present sufficient conditions for global exponential stability. Moreover, when there are unstable subsystems in this class of switched systems, we obtain some results on stabilization of this class of switched systems. (3)Stability and estimates of the region of attraction of a class of continuous-time switched systems with triangular forms are addressed. We first give sufficient conditions for global asymptotic stability under arbitrary switching signals of switched systems with triangular forms, and then we estimate the region of attraction of switched systems with triangular forms. Various examples are presented to illustrate these estimates.(4)Stability and estimates of the region of attraction of a class of discrete-time switched systems with triangular forms are also studied. We first give a result on global asymptotic stability of switched systems under arbitrary switching signals with triangular forms, on the basis of the result we also present suffiecient conditions which are easily checked for its global asymptotic stability under arbitrary switching signals, and then we estimate the region of attraction of this class of switched systems with triangular forms. Some examples are presented to illustrate these estimates.