Control And Synchronization Of The Fractional-order Chaotic Systems

The theory of fractional-order derivatives can be dated back the17th century, and developed comprehensively in the20th century due to its application in a wide variety of scientific and technological fields. On the other hand, it has been attracted more attentions on the chaotic phenomena for non-linear system. Especially, the conception of chaotic control and the conception of chaotic synchronization have been established in1990. More and more attentions on chaotic control and chaotic synchronization have attracted interest of many researchers, and some applications have been pointed. In recent years, study on the dynamics of fractional-order differential systems has attracted interest of many researchers. It is demonstrated that some fractional-order differential systems behave chaotically. Many researchers studied the chaotic control and chaotic synchronization for fractional-order chaotic systems too. But, on the control and synchronization of the fractional-order chaotic systems, the theory of control and synchronization still need further development, and the scheme of control and synchronization still need to be further improved.Motivated by the above discussion, based on the theory of chaos control and chaos synchronization, and the theory of mathematics, physics, automatic control, control and synchronization of the fractional-order chaotic systems are further considered in this paper. Some novel schemes on synchronization and control for fractional-order chaotic systems are proposed. To illustrate the effectiveness of the proposed schemes, their numerical simulations are performed. The numerical simulations demonstrate the validity and feasibility of the proposed schemes.