Research On Synchronization Control Methods Of Uncertain Fractional Order Chaotic System

Chaos theory is the most important research topics in nonlinear science,it mainly explores the chaotic dynamical behavior,and it explains many phenomena in nature and human society.With the development of research on fractional order calculus theory,the research of chaotic systems also extends to fractional order.The fractional differential equation simplifies the physical model,it improves the construct and control ability of the dynamic system.On the other hand,owing to the fractional order chaotic systems have all dynamic characteristics of the integer order chaotic systems and could show the essence of the real problem intuitively,and it has great application prospect in the field of secure communication and control engineering,so the synchronization control of fractional order chaotic systems has become a hot topic in the field of nonlinear science recently.In this paper,we do some profound theoretical analysis and exploration on the synchronization control problem of uncertain fractional order chaotic systems.Combining theoretical analysis and numerical simulation,we verify the feasibility of the proposed new synchronization control methods for fractional order chaotic systems.The main work of this paper are as follows:1.The lag dual synchronization of fractional order chaotic systems is realized.Based on the fractional Lyapunov stability theory,a lag dual synchronization control method of fractional order chaotic systems is proposed and an sufficient condiction is derived to realize the lag dual synchronization of fractional order chaotic system.By numerical simulation,we verify the sufficient condiction of the lag dual synchronization of fractional order chaotic systems is feasible.2.The adaptive sliding mode synchronization problem of fractional order chaotic systems is studied.Firstly,the fractional integral sliding mode surface with strong robustness is introduced,and then an appropriate controller is designed.The correctness of the proposed control strategy is analyzed based on fractional Lyapunov stability theory.The numerical simulation results show that the asymptotic synchronization can be realized between two fractional order chaotic systems with the proposed control method.3.The hybrid projective synchronization problem of fractional order chaotic systems is studied.A new synchronization control strategy is introduced to realize the hybrid projective synchronization for uncertain fractional order chaotic systems by using the adaptive sliding mode control method.The simulation results of fractional order chaotic systems show the effectiveness of the proposed method.