Theoretical Researches On Control And Synchronization Of The Chaotic Systems

This paper focuses on the chaotic systems, aimed at achieving chaos control and synchronization.Firstly, we analyze systemically the international actualities of the research and formulate the basic theory of chaos dynamics.Secondly, we illuminate the well-known OGY control method to the point and present a example by computer simulation. It usually takes chaotic systems a long time to enter the control window in the method. So we present a strategy of targeting chaos to increase greatly the efficiency. To overcome the defect of the discrete variable feedback method, the continuous variable feedback method is presented. It can stablize the chaotic trajectory to the periodic orbit whether by local control or global control. The simulation result show its algorithm is simple and the control effect exceeds the OGY control.Thirdly, considering all of the states of the systems can not be measurable in fact, we present the observer-based control method. We design an nonlinear observer for the forced chaotic oscillators and focus on two control problems, i.e. to change the dynamics of the given forced chaotic oscillator into the desired dynamics and to make the system track an reference signal given arbitrarily. The computer simulation result illustrates the effectiveness of the proposed method.Finally, the problem of tracking control and synchronization of the systems is researched. The controller consisting of the reference signal feedforward and the state feedback can make the systems track an reference signal given arbitrarily. So the self-synchronization and diverse structure synchronization of the systems can both be achieved. We transplant the adaptive approach of chaos control to chaos synchronization and can recognize the parameters of the parameter-unknown systems and increase the robustness of the systems to parameter mismatch and noise disturbance. The presented synchronization strategy of combining adaptive control with pole assignment integrates the two advantages into a coherent whole: It can both accelerate theconvergence of the closed-loop systems and make the systems robust.