Research Of Methods For Chaos Control And Synchronization

There has been some increasing interest in recent years in the study of controlling chaotic nonlinear systems and chaos synchronization scientific and technological areas, such as in the physics, mathematics, and engineering communities, etc.In general , for chaos control, our interest is in studying the problem of how to design a feedback controller to drive a chaotic trajectory of the equation to a predesigned target position. On the other hand, we refer to synchronization of chaos as a process wherein two chaotic systems adjust their motion to a common behavior, due to coupling or forcing. In this paper, we present some ideas and techniques for the control and synchronization of chaotic continuous system from the viewpoint of classical control theory.The main originality in this paper can be summarized as follows: An constructive method for chaos synchronizationAn effective approach based on Backstepping method for chaos synchronization is proposed. There are some advantages in this method for synchronizing chaotic systems, such as (a) the synchronization error is exponential convergent; (b) only one variable information of master system is needed; (c) it presents a systematic procedure for selecting a proper controller. Numerical simulations show that the proposed theoretical approach is very effective.Adaptive synchronization of chaotic with uncertain inputs The synchronization of chaotic system with inputs including an unknown constant parameter, furthermore, whose only one variable can be measured, has been studied in this chapter. A constructive method has been applied to the design of an adaptive controller, which can adjust the corresponding parameter in the slave system being eventually approached the unknown parameter of the master system, in the course of this, also make the errors between the master system and the slave system converge to zero asymptotically. This method is illustrated by its application to the modified Chua circuit.The conditions of chaos synchronization for a class of systems using constant gain feedback methodThe constant gain feedback technique has been applied to chaos control and synchronization for some time, however, conditions for such application have not been clearly addressed in the literatures. In this paper, chaos synchronization based on the constant gain feedback method is dealt with for a class of chaotic systems in terms of lower-triangle representation. In this case, as long as the feedback gain is sufficiently large, the control signals, which need that only one variable of the master system is available, can drive the errors converging exponentially to zero.