Control And Synchronization Of Chaotic System

Recently, as an important branch of nonlinear systems, the synchronization of the chaotic systems have potential application in many fields such as secure communication and information processing. However, the plants are easily influenced by uncertainties in application of engineering at actual, such as modeling error, parameter time delay,disturbance and so on. As a result, we can not describe the dynamic behavior with the precise mathematical models. As the development of the control theory, many effective control algorithm have been developed to solve the uncertain systems on condition that known control coefficient and the the upper bound.Considering the parameters and uncertain part are partially known or unknown in the practice application, the paper mainly studies the robust adaptive controllers design for uncertain nonlinear systems and the unified chaotic systems. A priori of the bound of the time-varying parameters and control coefficient is not required, and use strictly positive integral function in the control law. To eliminate the influences of the environmental changes and disturbance,the design controllers could on-line estimate the unknown parameters. The main results are as follows:(1)The problem of robust adaptive tracking control for uncertain nonlinear systems with time-varying parameters is investigated, two control algorithms are presented such that the systems asymptotically or exponentially tracks the desired trajectory. Then using the Lyapunov theory, the boundedness of closed-loop signals and systems stability is shown. The effectiveness of the control methods is demonstrated by the application to nonlinear chua’s circuit.(2)This study concerns the problem of robust adaptive synchronization control for uncertain unified chaotic systems with parameter variation, system uncertainties and disturbances. Design the proper control law and update law based on the Lyapunov theory to show the asymptotically or exponentially synchronization between drive system and response system. Lorenz systems、Chen systems and L ¨u systems are provided to prove the effectiveness of the control method.