Reaserch Of Some Problems In Synchronization And Control Of Chaotic Systems

As an important branch in the field of intelligent control, the technology of chaotic control and synchronization has received more and more attention in recent years. Some correlative issues in this area are studied in this paper, such as the chaos control and anti-control problems, the linear and nonlinear generalized synchronization of chaotic systems, synchronization and generalized synchronization of a class of fractional order chaotic systems. The main work in this paper is summarized as follows.(1) Chaos control and anti-controlFirstly, the writer presents the chaos control for R(o|¨)ssler system, the control strategy directs the chaotic motion of the Rossler system to any desired fixed point based on feedback control method. Then, tracking control of Chen system is adopted. Simulations and theoretical proof with Chen system are studied, and the results can prove the tracking controller enable the enor signal exponentially to converge to zero and the output signal can track all kinds of reference signals under tracking control. Last, anti-control of chaos of Coullet system is studied in this paper based on various numerical simulations, such as phase diagram, bifurcation diagram, Lyapunov exponents spectrum. By addition of an external linear term, we can obtain anti-control of chaos. Numerical simulations show that the new system's behavior can be convergent, divergent, periodic, chaotic and hyperchaotic when the feedback parameter varies.(2) Linear and nonlinear generalized synchronization of a class of chaotic systems Secondly, the linear and nonlinear generalized synchronization of chaotic systems isinvestigated. Based on the modified state observer method, a new synchronization approach is proposed with more extensive application scope. The proposed synchronization scheme can realize the linear and nonlinear generalized synchronizations of same dimensional or different dimensional chaotic systems. Sufficient conditions of global asymptotic generalized synchronization between the drive system and the response system are gained on the basis of the state observer theory.(3) Synchronization and generalized synchronization of a class of fractional order chaotic systemsFinally, based on the modified state observer method, synchronization and generalized synchronization of a class of fractional order chaotic systems are presented. The two synchronization approaches are theoretically and numerically studied and two simple criterions are proposed. By using the stability theory of linear fractional order systems, suitable conditions for achieving synchronization and generalized synchronization are given.