Variable Exponential Synchronization Of Chaotic Systems

In this thesis,the variable exponential synchronization of chaotic systems with external disturbances is mainly studied by using saturation control.Chaos synchronization has been widely studied due to its broad application prospects.Exponential synchronization is an important synchronization mode.The convergence rate of most existing exponential synchronization schemes is a fixed constant.However,from the practical application point of view,people hope that the system can achieve exponential synchronization as soon as possible and the convergence rate can be adjusted according to the actual situation.On the other hand,in practice,some actuators may reach saturation due to the physical limitations.When the actuator is saturated,the performance of the control system may be seriously damaged.In order to improve the control performance,the situation of input saturation should be included in the design of the control system.Therefore,it is of great theoretical and practical significance to study the variable exponential synchronization of chaotic systems by using saturation control.The main content and structure of this thesis are as follows:The first chapter presents some classical definitions and the research status of chaos synchronization,and then briefly summarizes the main content of this thesis.In chapter 2,a new scheme of variable exponential control and synchronization for three-dimensional chaotic systems with external disturbances is proposed by using saturation control.In the proposed scheme,a novel coordinate transformation method is designed and some new saturation controllers are given,which can not only make the system converge to zero exponentially with variable decay rate λ,but also allow the designer to directly determine the boundary of the control input signal to improve the control performance.In Chapter 3,the robust exponential synchronization of a class of n dimensional chaotic systems with variable convergence rate is studied.By using the appropriate coordinate transformation to transform the exponential synchronization problem into the asymptotic stability problem of the error system,some sufficient conditions for the system to achieve variable exponential synchronization is obtained via the Lyapunov stability theory.The summaries of this thesis and future research directions are proposed in Chapter 4.