Chaos Synchronization And Control Based On Observer And Adaptive Method

Nonlinear science is a foundational discipline which concerns the common properties of nonlinear phenomena.Particularly,Chaos theory is one of important subdiscipline of nonlinear science.People begin to study the problems of chaos control,chaos synchronization, for its complex dynamics behavior.The author has studied chaos control and synchronization based on observer and adaptive method,using the methods of theoretical analysis and numerical simulation.The main originality in this paper can be summarized as follows:Firstly,the author proposes a novel hyperchaos system.It is of high Lyapunov exponent and non-symmetry.And the behavior of the novel system can be periodic,chaotic and hyperchaotic as the parameter varies.And the author designs a novel observer for the new system.It only needs two signals of master system.Based on the modified nonlinear state observer algorithm and the pole placement technique,a synchronization scheme is designed. The generalized projective synchronization of the hyperchaos system is achieved by using this observer controller.It is demonstrated the effectiveness of the proposed scheme in therom.Secondly,the author studies the method of dual synchronization of Qi system and R(?)ssler system.The author not only realizes the dual synchronization but also identify the unknown parameters of system.The validity of the method is demonstrated in theory.Thirdly,the adaptive synchronization and parameters identification method of a class continual and discrete chaos system is studied by the author.Based on Lyapunov function, LMI theory and map therom,the author designs novel controller and update rules.The synchronization between drive system and response system can be realized by the controller and update rules.Meanwhile the parameters of response system can be identified.The validity of the method is demonstrated in theory.Lastly,Based on Yassen chaos system,the author proposes a novel hyperchaos system. At the same time,the author analyzes the property and dynamic behavior of the novel system. The state of the system model can be changed from chaos to hyperchaos with the parameter varies.The adaptive scheme and observer synchronization are designed to realize the adaptive and lag synchronization between different hyperchas systems.