Chaos Control And Synchronization Based On Input-to-state Stable

The sensitivity to changes in initial conditions, a kind of intrinsically character, and complexity of chaotic dynamical system make the research on chaos control and synchronization to be more challenging. Research on chaos control and synchronization becomes a new focus in nonlinear science fields. Many methods were advanced to control chaos over the last ten yeas, however, each method has its weak poits, there is not a method which can be used to control all the chaotic systems.The main content of this paper contains the control and synchronization of continuous chaotic dynamical system. ISS method was proposed based on the theory of input-to-state stable. Some nonlinear feedback controllers were designed to globally stabilize the unstable equilibria of a new chotic system. Chaos synchronization was also obtained by using ISS method. The main contributions are as following:1) Introduced the evolution process of chaos and chaos control. Concepts of chaos and some methods of chaos control were presented.2) Introduced the theory of input-to-state stable and proposed ISS method.3) ISS controllers were designed to globally stabilize the equilibria of the new chaotic system. The new chaotic system has five unstable equilibria. The origin can be stabilized by using linear feedback control. Nonlinear ISS controllers were designed to stablilize the other four equilibria. Chaos synchronization was obtained by ISS control.4) Numerical simulations verified the effectiveness of ISS control in stablizing the equilibria and chaos synchronazation.