Control And Synchronization Of Several Autonomous Chaotic Systems

Recently, chaos theory as one of important subdisciplin of nonlinear science, combined with the biology, chemistry, production engineering, and computer science and so on, displayed very widespread application prospect. Therefore, it's significance to analysis the characteristics of the non-linear system and to research the controlling methods of it either in thorey or in application in engineering.This paper,using a combination method of theoretical proof and computer numerical analysis,mainly do the following researches:(1)The author studies control and synchronization problems of a new three-dimensional. Linear negative feedback and nonlinear control methods are used respectively to achieve chaotic control and self-synchronization, and gives a theoretical proof. Numerical simulation results further prove the effectiveness of the control and synchronization methods.(2) A nonlinear controller via backstepping design is presented to achieve projective synchronization. By changing the scale factor of projection synchronized, we get the response-system to obtain an arbitrary ratio of the original drive on the output signal of chaotic systems. The numerical simulation results demonstrate the validity and feasibility of the proposed controller.(3)The author studis the problem of chaos synchronization of a novel chaotic dynamical system. Backstepping design and active control methods are used to achieve synchronization between two identical systems based on the Lyapunov stability theory. Then, Proposed a systematic design procedure to synchronize the novel autonomous chaotic systems based on the nonlinear state observer design and the pole placement technique.Numerical simulations are provided to show the effectiveness and advantage of the analytical results.(4) The author studis the problem of chaos anti-synchronization of an energy resources demand-supply system. An improved active control method is proposed.This method can reduce the control signal effectively. Based on this method, a suitable active controller is designed to achieve anti-synchronization of the energy resources demand-supply system chaotic system. Numerical simulations are provided to show the effectiveness and advantage of the analytical results.