Research On Some Methods Of Chaotic Control And Synchronization Of Complex System

Research on chaotic control and synchronization method of complex nonlinear system is one of the hot issues of nonlinear science. At present, the chaotic control and synchronization method of the real/complex single system in complex nonlinear system and complex networks has made a lot of research results. However, the controller design of chaotic single system is multidimensional, step complicated and large amount of calculation. The study of single system synchronization are all finite time completely synchronization. Therefore, in this paper, the further research on the chaos control and synchronization of single system, synchronization of complex system.In this thesis, our main work is as follows:(1) Further research on the chaotic control of real variable chaotic system, puts forward the inverse optimal control method for controlling chaos of the permanent magnet synchronous motor. According to inverse optimal control method and Lyapunov stability theory proves that the correctness of controller. And puts forward the problem of finite time control for the unified chaotic system base on triangle stability theory and hybrid projection synchronized methods, procedures simple implementation easy and can effectively realize the finite time chaos control. With the support of the study above, put forward LMI fuzzy finite-time control. According to the theory of finite time stable and Lyapunov theory of stable proves the finite time controllers can achieve chaos control in a finite time. Simulation results further validate the above correctness of the schemes.(2) Further research on finite time projective synchronization, put forward the method of hybrid projective synchronization and function projective synchronization for the unified chaotic systems. Based on the Lyapunov stability theory and the theory of finite time stable, the finite time controllers are designed, which can make chaotic unified chaotic systems realize hybrid/function projective synchronization. The numerical simulation further verifies the above correctness of the schemes.(3) Further research on the synchronization of the complex system and complex network, put forward the hybrid complex (function) protective synchronization of the complex system, and synchronization of the complex system with disturbance. According to the theory of Lyapunov stability, feedback controllers are designed by the adaptive method. The theory proves that the above two kinds of controller can make the synchronization error of the complex system gradually tends to zero. Finally, put forward adaptive hybrid function projective synchronization of the complex network, the feedback controller is designed base on Lyapunov stability theory, the theory proves that the controller can make the mixed function projective synchronization error gradually tends to zero. The numerical simulation further verifies the correctness of the schemes.