Control And Synchronization Of Several Typical Autonomous Chaotic Systems

Nonlinear science is a foundational discipline which concerns the common properties of nonlinear phenomena. And chaos theory is one of important subdisciplines of nonlinear science. The research studies the relative problems of chaos control and chaos synchronization:The synchronization problem of the unified chaotic system is studied. Three different methods, linear feedback method, non-linear feedback method and impulsive control method are adopted. Based on the Lyapunov stability theory and impulsive control method, the conditions of synchronization are obtained.Adaptive control and synchronization of the unified chaotic system with known or unknown parameters is researched. Based on the Lyapunov stability theory, an adaptive controller is designed. It can control the unified chaotic system with known or unknown parameters to the stability and make the dynamical system and the response system with known or unknown parameters asymptotically synchronized.Unified chaotic system is used as an example to research adaptive full state hybrid projective synchronization method. An adaptive controller is designed which can make the states of the dynamical system and the response system with known or unknown parameters asymptotically full state hybrid projective synchronized.The state observation problem of hyperchaotic R(o|¨)ssler system is investigated. Based on the time-domain approach, a simple observer for the hyperchaotic R(o|¨)ssler system is proposed to guarantee the global exponential stability of the resulting error system.The generalized projective synchronization problem of a class of chaotic system is studied. Basing on state observer method, a scheme is proposed to drive hyperchaotic R(o|¨)ssler systems get generalized projective synchronization.Based on the stability theory of fractional order systems, the paper analyses the synchronization conditions of the fractional order chaotic systems with activation feedback method. And the synchronization of commensurate order hyperchaotic Lorenz system of the base order 0.98 is implemented based on this method.