Control And Synchroni-Zation Of Continuous-Time Chaotic Dynamical Systems

Chaos is a kind of quasi-stochastic dynamical behaviors of determinate nonlinear system. It has attracted common attention and has been extensively studied for last decades. While chaos control and anti-control are the basic problems of the application of chaos. To deal with these problems, a lot of effective methods have been produced. But the sensitivity to changes in initial conditions, a kind of intrinsical character and complexity of chaotic dynamical system make the research on the chaotic control theory to be more challenging.In this thesis, the problems of the chaos control, anti-control and synchronization are studied. The detail is clarified as follows:First of all, the paper discusses a new system-----circle-linked system, the problem about chaos anti-control of linear and nonlinear circle-linked systems is considered via the method of the nonlinear feedback, according to the nature of anti-control of a chaos system. By introducing tracking control subtly, the chaos anti-control of the two circle-linked systems is successfully realized.Secondly, the problem of exponential lag synchronization of a three dimensional chaotic system is studied,and the method to design control laws is given via linear feedback control and Lyapunov stability theorem. At last, we give the numerical simulation and electric experiment to demonstrate the effective of the control method and the available of the control laws.Thirdly, the paper constructs a new continuous chaotic system, and its basic dynamical behaviors are briefly described. Having proved the system under consideration is different from other chaotic systems. Then we study the synchronization of this new system by adaptive feedback control.Finally, the problem of Robust control for a class of uncertainty and time delay chaotic system with input saturation is proposed. We have a perfect method to deal with the item of saturation and design a controller to make the chaotic system to its one of unstable fixed points by using standard feedback control (SFC). We give control laws by LMI, and the designing of the Lyapun- ov function is also unique. At last, the feasibility of the method is described by the well-known Lorenz system.