The Research On Control And Synchronization Of Fractional-Order Chaotic Systems

The theory of fractional-order derivatives can be dated back to the 17 th century,and developed comprehensively in the 20 th century due to its application in a wide variety of scientific and technological fields.On the other hand,chaotic systems always exist in nonlinear dynamic systems,and have been well studied in many fields such as physics,finacial and life science.Considering the fact that the dynamic behaviours are closely related to the system order and the historical memory effect for fractional operator,the dynamic behaviours created by fractional-order chaotic system are more complex that that of the tranditional integer-order chaotic system,it has been widely applied in the fields of image processing and secure communication.Recently,the research on control,synchronization and application of fractional-order chaotic system has received a increasing attention with the rapid development of the computer engineering.However,the domestic and overseas scholars start their research later,so the theory of control and synchronization still need further development,and the scheme of control,synchronization and application still need to be further improved.Therefore,based on the previous works,this paper studies the problems of control,synchronization and application of fractional-order chaotic system.The specific work and research result can be briefly described as follow:Firstly,this paper proposed two different methods separately for the control of fractional-order chaotic system.First of all,the problem that non-fragile T-S fuzzy control of fractional-order unified chaotic system is investigated;In the second part,another problem that finite-time stabilization of a class of fractional-oder nonlinear system is investigated.In the final part,the effectiveness of the proposed method is verified by numerical simulation.Secondly,this paper proposed two different synchronization schemes for fractional-order chaotic synchronization.In the first part,the problem that fuzzy adaptive function combination projective synchronization of three fractional-order chaotic systems with some structure and order is investigated,In the second part,the problem that adaptive projective synchronization of two fractional-order chaotic systems with different structures and orders is investigated based on active control method..At last,the effectiveness of the proposed method is verified by numerical simulation.Finally,this paper designed a secure communication scheme based on Multiswitch synchronization of two fractional-order chaotic systems with different structure and different orders.The proposed secure communication scheme has a good ability of transmitting information and a characteristic of high security.At last,sine function and square signal are supposed as useful signal and the effectiveness of the proposed scheme based on synchronization of fractional-order chaotic system is verified by numerical simulation.