The Application Of The Exact Linearization Controlling In The Chaos Control Of The Dynamic Systems

Controlling chaos has become an important part of nonlinear science theory since Ott. ,Grebogi and Yorke proposed the O.GY methods in 1990, it has become a hot topic and important problem for the theroyand application of controlling chaos. Many effective methods for controlling chaos have been proposed in the insides and aboard, such as: parameters disturbation methods, the feedback way, the time-delayed methods, etc. Among these methods, the feedback way has quite broard application, and has very good controlling effect. In this paper, introduce the methods of exact linearization cotrolling, which has gamed many good results in thedry and numery as to some simple ordinary differential systems, but the work about applying the exact linearization controlling in the control of some complex ordinary differential systems and partial differential systems has not been carried out. In this paper, the second chapter introduces the reducing idea of inertial manifolds and approximate inertial manifolds, and discuss the similarity reduction of KS equation.The third chapter introduces the basical idea and theory of the exact linearization controlling, then use this methods to control chaos of an ordinary differential system CHEN equation and apply the exact linearization controlling method to control the chaotic behaviours, i.e.controlling the chaotic states to steady states. The fourth chapter applies the exact linearization controlling method to control the approximate inertial manifolds of a partial differential system KS equation. This method can control the chaotic states into steady states and also can control the steady states into circle solutions. The CHEN equation and KS equation both have typical dynamical behavior and dynamical character. From the numerical results, we can find that the exact linearization controlling methods has quite good control effect when it is applied to controlling chaos to steady states and controlling steady states to circle solutions.Therefore this methods is a simple and effective way to the study of controlling chaos.