Research On Synchronous Control Methods For Fractional Order Chaotic Systems Base On Sliding Mode

Chaotic motion is a seemingly clutter but a quite rules of movement.Because chaotic system is extremely sensitive to initial value and similar to noise,it has a wide range of applications in communications,medical and economics.Fractional order chaotic system not only has the characteristics of integer order system,but also has the characteristics of historical memory.Its dynamic characteristics more complex than integer order system,so synchronous control research for fractional order chaos has a broad application prospect.This paper study the fractional order chaotic synchronization problem of having two same structure,different dimension and unknown parameters based on sliding mode control theory.Finally the research results of this paper are applied into the communication system.In this paper,the main research work as follows:(1)Research on synchronous control methods of the same dimension and structure of fractional order chaotic system.First through the drive and response systems'status obtains the synchronization error system.In order to facilitate the design of controller,synchronous error system is linearized by active control thoughts,and then the controller is designed based on state feedback and stability theory of fractional order linear system.Due to the above method to design control system has poor ability to resist external disturbance and long synchronization time,so a fractional order sliding mode surface and sliding mode controller is designed on the basis of the active control to accelerate the synchronization time and enhance the robustness of the system.Through theoretical proof and numerical simulation on Matlab\Simulink to verify the effectiveness of the design method,and active sliding mode controller has better control effect.(2)Research on synchronous control methods of two different dimensions and unknown parameters of fractional order chaotic system.First an appropriate matrix is chosen,and this matrix can map the drive system to the response system.Then a synchronization controller is designed based on the mapping of two chaotic systems.Adaptive control method can identify parameters of system and automatically adjust some parameters of the controller to reach the requirement of control.So first an adaptive controller is designed.Considering the fast response and strong robustness of system,a controller is designed based on adaptive control and sliding mode variable structure control.Through theoretical proof and numerical simulation on Matlab\Simulink to verify the effectiveness of the design method,and adaptive sliding mode controller has better control effect.(3)Based on chaotic secure communication technology,this paper applies the research results to secret communication.Due to useful signal with a simple superposition of a chaotic signal in the traditional chaos masking technology,making the secret result is not good.This paper uses the improved chaos masking technology,and applies the chaotic synchronization research of this paper to communication system.Through numerical simulation on Matlab\Simulink verify the effectiveness of the design method.