Synchronization Control Of Fractional-order Chaotic System

Chaotic motion is a complex nonlinear motion, whose trajectory of orbits in the phase plane is very complex but not stochastic. It has been intensively studied during the last three decades. Chaotic behaviour is commonly detected in a wide variety of physical systems, such as electrical, mechanical and thermal systems. And because of the dynamic properties of chaos signal such as ergodicity, aperiodic, uncorrelated, broad band and picture encrypt systems, so chaos control and synchronization has become a very important topic in chaos science due to its potential application in secure communication.The study on fractional-order calculus theory has a history more than 300 years. However, the application of fractional calculus in physics and engineering is just a recent foucus. In this paper, we choose the continuous-time chaotic systems as the objects to analysis the chaotic behaviors of the fractional-order nonlinear dynamical systems and address the problems of chaotic control and synchronization method for nonlinear systems. Theoretical analysis and numerical simulation results are presented to demonstrate the effectiveness and feasibility of the proposed method. The main achievement contained in the research is as follows:The article mainly studied the chaos synchronization of fractional-order dynamical systems. Although many kinds of good synchronization modes for ingegral order chaotic dynamical systems have been invested, these modes can not be completely applied to fractional dynamics systems. In this paper, we mostly analyses three synchronization methods, state observer, nonlinear feedback and generalized synchronization.State observer:We first studied the definition of nonlinear state observer. Based on the theory of integral state observer, we designed the linear and nonlinear observer scheme to reconstruct the state variables of the original system. Furthermore, the synchronization of chen system is taken as example to illustrate the effectiveness of state observer. We get that the state observer can be used in the fractional-order systems and the method is simple and easy to achieve.Nonlinear feedback:This method makes the nonlinear system linearlized. The controller is obtained based on the stability theory of linear fractional-order systems. The synchronization of fractional-order chen system and the hyper new and hyper chen systems are taken as examples to illustrate the effectiveness of proposed method. The method can be applied to solve synchronization problems of several classes of fractional-order chaotic systems and the controller is systemic.Generalized synchronization:Based on the stability theory of linear fractional-order systems and the tracking control methods, the appropriate controller is proposed to obtain two fractional-order chaotic systems'generalized syschronization. It makes the synchronization controll problem not only limite to the synchronization of complete synchronization. Accordingly, the research field of fractional-order chaotic synchronization was broaden.