Study Of Synchronization For The New Fractional-order Hyperchaotic System Based On Sliding Mode Variable Structure Control

The theory of chaos control and synchronization is an important part of the nonlinear field.Fractional-order hyperchaotic systems are more complex than integer order chaotic systems and have wide application value in many fields,such as physics,secure communication.In recent years,chaos control and synchronization have been a hotspot of research,many chaos control and synchronization methods have been proposed.However,the application of traditional chaotic synchronization methods is interfered by many external factors so that these methods are easy to be destroyed.The sliding mode control theory has received wide attention in the field of chaos control because of its robustness.It has been applied widely in the field of chaos synchronization after the development of many years.In this paper,based on sliding mode variable structure control theory,the synchronization of fractional-order hyperchaotic systems is studied.First,we perform a brief introduction on the research situation of chaos synchronization and the sliding mode variable structure control theory.Then,the sliding mode controller is designed by combining the sliding mode control method and the traditional active control method.It achieves the synchronization of a new fractional-order hyperchaotic system.And its speed is obviously faster than that of the traditional active control method.Given that the controller is complex,we proposed a new sliding mode surface and designed a new sliding mode controller according to the sliding mode control theory.The structure of the controller is simple and the time that the systems achieve synchronization is shorter.Finally,based on the matrix theory,the controller is designed by making use of active control method to achieve the synchronization of the new fractional-order hyperchaotic system with different structure.Compared with the traditional stability theorem,this method need not calculate the Lyapunov function and it is simple.Based on this we combined matrix theory and sliding mode control method,the new sliding mode controller is designed.The experiment results show that we take advantage of sliding mode variable structure control method not only need not calculate the Lyapunov function,but also improve the synchronization speed of the systems and the systems are still fast synchronized under weak disturbance of external factors because of its robustness.The results of circuit simulations and numerical simulations confirm the effectiveness of the controllers.