Synchronization Control Of Autonomous Chaotic Systems

Nonlinear science is a foundational discipline which concerns the common properties of nonlinear phenomena. Particularly, chaos theory is one of important subdisciplines of nonlinear science. The relative problems of chaos synchronization control are studied in this thesis using the methods of theoretical derivation and numerical simulation. The main achievements contained in the research are as follows:Firstly, anti-synchronizations of three-dimensional autonomous chaotic systems are analyzed. The anti-synchronizations of a class of three-dimensional autonomous chaotic systems i.e. Lorenz system, Chen system and Lu system with one another are achieved via active control. The form of the controller is simple and implemented easily. The convergence rate of the controller is very fast and the control range is very broad.Secondly, the synchronization control of a new chaotic system called Lorenz-like system is investigated. Based on the Lyapunov stability theory, an adaptive controller and the parameters update rule are designed. It is proved that the controller and update rule not only can achieve self-synchronization of Lorenz-like system but also can make the Lorenz-like system asymptotically synchronize with the Rossler system, and further identify the uncertain system parameters.Thirdly, projective synchronizations in autonomous chaotic systems are presented. Based on the stability criterion of linear systems, a new approach for constructing chaotically projective synchronization is proposed. The projective synchronizations of Lorenz system, Rossler system and hyperchaotic Chen system are achieved using the linear separation method. The proposed method is not only simple and implemented easily, but also need not design Lyapunov function and enables to realize projective synchronization in a general class of nonlinear systems without the limitation of partial-linearity.Lastly, a systematic design procedure to lag-synchronize a class of chaotic systems based on techniques from the state observer design and the pole placement technique is presented. The lag synchronizations of Newton-Leipnik system and hyperchaotic Chen system are achieved by using nonlinear observer control. Numerical simulations are provided for illustration and verification of the proposed method.