Research On The Output Tracking And Regulation Problem Of Switched Systems

Switched systems are an important class of hybrid systems, which are of great signif-icance in theory and have wide applications in engineering practice. Due to the interaction of continuous dynamics and discrete dynamics, the behavior of such systems become very complicated, a lot of problems deserve investigation. At present, most of the results refer to switched systems focus on stability.This dissertation studies the output tracking and regulation problem of several kinds of switched systems. Because theories and approaches for non-switched systems are not directly applicable to the problems of output tracking and regulation for switched systems, the study is even more difficult. By virtue of the multiple Lyapunov function method and the average dwell time method, sufficient conditions are given for the output tracking and regulation problem of switched systems to be solvable, a theory framework of output regulation problem for nonlinear switched systems is established. The main contributions of this thesis are as follows.1. The problem of robust output tracking control for uncertain cascade nonlinear switched systems with external disturbances is studied. A sufficient condition for the out-put tracking problem of switched systems to be solvable is given in terms of the average dwell-time scheme and linear matrix inequalities where no solvability of the output track-ing control problem for all subsystems is assumed. The controllers are designed based on a variable structure control method in order to conquer the uncertainties in the output tracking problem.2. The H∞ output tracking control problem for a class of cascade nonlinear switched systems is investigated. Under various assumptions, the solvability conditions for the H∞ output tracking control problem are developed and the rules of switching are designed, based on the multiple Lyapunov function method and the average dwell time method, respectively. According to the multiple Lyapunov function method, the solvability of the problem for subsystems is not assumed. The use of the average dwell time method such that H∞ output tracking is achieved, when the zero dynamics is unstabilizable under an arbitrary switching.3. Incremental passivity and the output tracking problem of nonlinear switched sys-tems are investigated. The concept of incremental passivity for switched systems is giv-en using the proposed weak-storage functions. Furthermore, conditions for a nonlinear switched system to be incrementally passive are obtained without the requirement of the incremental passivity conditions for subsystems. It is shown that once the incremental passivity is assured, the output tracking problem for nonlinear switched systems is solv-able via the designed controllers, even though the problem for none of subsystems is solvable.4. The problem of output regulation for a class of continuous linear switched systems is discussed. Firstly, sufficient conditions for the problem to be solvable are given via the multiple Lyapunov function, where the problem for each subsystem may not be solvable. Secondly, based on the average dwell time method, the solvability conditions are also presented. The main results are obtained based on the full information feedback and the error feedback, respectively. Furthermore, based on the solvability conditions, the designed controllers are given.5. The problem of output regulation for a class of nonlinear switched systems is studied. Sufficient conditions for the problem to be solved are presented in terms of the theory of centre manifold and the average dwell time scheme. These conditions are obtained based on full information feedback controllers and error feedback controllers, respectively. The results extend the output regulation theory for nonlinear non-switched systems to nonlinear switched systems.6. The output regulation problem for a class of nonlinear switched systems is ad-dressed based on the concept of geometric steady states. First of all, the multiple Lya-punov function method is adopted to design a switching law, which solves the problem without the problem solvability of any subsystem. Then, in the sense of an average dwell time, another solvability condition for the problem is presented with respect to a family of switching signals which satisfies the average dwell time. Moreover, an explicit expression about the average dwell time is given.Finally, the results of the dissertation are summarized and further research issues are point out.