Research On Control Of A Class Of Time-delay Chaotic Systems

Since Mackey and Glass first investigated chaotic systems with time-delay in 1977,there has been increasing research interests in chaos control for nonlinear dynamic systems with time delay.Now time-delay chaotic system has been one of the most hot research topics in the area of control theory and control engineering.In this thesis,the delay-dependent optimal guaranteed cost control problem is studied for a class of time-delay chaotic systems by applying the linear matrix inequality(LMI) technique.A new design method is proposed for the memoryless state feedback guaranteed cost controllers,and some better results are derived as compared with the existing ones.The main work and contributions of the thesis are as follows:1.The research significance,present research situations and analysis and synthesis techniques of time-delay chaotic systems are discussed.Some preliminaries are presented,which include the basic knowledge about the LMI technique,the delay-dependent analysis and synthesis methods for time-delay systems and the guaranteed cost control approach.2.The delay-dependent analysis and synthesis methods for time-delay systems are thoroughly discussed.The conservatism of the various delay-dependent approaches are compared and illustrated by a numerical example,and it is concluded from the comparison that the free matrix approach and the integral-inequality approach are of less conservatism and are suitable methods to study the analysis and synthesis problems for time-delay systems.The integral-inequality approach is chosen as the main approach to investigate the analysis and synthesis problem for the linear time-delay systems under consideration. 3.Some commonly used approaches for chaos control and synchronization are discussed in detail by a thorough study on the present research situation and future development tendency of this area.A variety of approaches are now available in the literature to study the chaos control problem,some main approaches are OGY method, series feedback control,adaptive control,intelligent control,pulse control,optimal control and so on.Methods for chaos synchronization include the drive-response method,active-passive decomposition method,cross-coupled method,variable feedback synchronization method and adaptive synchronization method.4.The delay-dependent optimal guaranteed cost control for a class of time-delay chaotic systems is studied by considering a given performance index of quadratic form.Sufficient conditions for the existence of the memoryless state feedback guaranteed cost controller and the corresponding design method for the controllers are derived by using the free matrix approach and the Lyapunov stability theory.The obtained conditions are delay-dependent,and are less conservative.The conditions are all presented in terms of LMIs,and thus can be effectively solved.5.Conclusions are given,and discussions on the studies for the time-delay chaotic systems are also presented.