Study On Several Problems Of Stability And Optimal Control Of Switched Systems

This dissertation concerns with some issues related to the study on several problems of stability, construction of objective function and solving of objective function of a class of switched systems. The main contributions are summarized as follows:The problem of optimal switching for a class of linear switched systems is investigated. The cost function with respect to the switching number, switching sequence, switching instants and control inputs of subsystems is presented, based on linear quadratic optimization and mixed-integer programming. The conditions for stabilization with arbitrary switching are presented based on multi-Lyapunov function technique. By genetic algorithms the cost function is solved. This is in contrast to search based algorithms where a fixed number of switchings is set a priori. In this approach, the optimal solution can be determined by solving the cost functional.Robust stabilization of a class of nonlinear switched systems with parameter uncertainty is investigated, all subsystems of this class of nonlinear switched systems are lurie systems. Based on multiple Lyapunov functions technique and Linear Matrix Inequality technique, the robust stabilization of this class of nonlinear switched systems is found.The problem of optimal switching for a class of switched systems is investigated. The cost function with respect to the switching number and switching sequence and switching instants is presented. An approach is got based on genetic algorithms, this approach imposes no restriction on the switching sequence or the number of switchings. This is contrast to search based algorithms where a fixed number of switchings is set a priori. In this approach, the optimal solution can be determined by solving the cost function.A new approach is presented based on dwell time and Gronwall-Bellman’s inequality, for solving input-to-state stability and optimal control problems of a class of switched systems. Constraint conditions on switching instants and switched number are transformed into linear constraints. A new form of objective function is constructed such that switched systems is input-state stability. Optimal results can be got by solving differential algebraic equations. Compared with the existing methods, the proposed method does not employ new variables and constructing input-to-state control Lyapunov function, and input-to-state stability properties are not required for all subsystems. It’s great convenient for optimal design of subsystem’s controller by using optimal control theory. Based on the multi-Lyapunov function approach, dwell-time approach and Gronwall-Bellman’s inequality, a new approach to input-to-state stability problems for a class of switched systems with time delay is presented. From the definition of input-to-state stability, necessary conditions under which a class of switched systems with time delay is input-to-state stable are obtained. Compared with the existing methods, the proposed method does not construct input-to-state stable control Lyapunov function, and input-to-state stability properties are not required for all subsystems. It’s great convenient for design of subsystem’s controller.