Research On Fractional Sliding Mode Control For A Class Of Fractional Order Nolinear Time-Delay Systems

In recent years,as more and more scholars have focused their attention on the study of fractional calculus,the application of fractional-order nonlinear systems in engineering practice and physics has been widely extended and deeply developed.Especially in the modeling problem of complex systems,the fractional-order calculus model is more accurate than the integer-order calculus model in the modeling of complex systems.In addition,because of the inevitable factors such as friction,mechanical or feedback delay in practical application,the time-delay always exists in the actual control system and seriously affects the dynamic characteristics of the system,which makes the system more complex.So it becomes a hot topic to study the fractional-order nonlinear time-delay systems in the field of fractional orders.On the other hand,in recent years,the widespread application of system synchronization in engineering has attracted more and more attention,especially in the field of secure communications.However,there are not many researches on the synchronous control problem of fractional-order nonlinear time-delay systems.The synchronization control of fractional-order nonlinear systems has become a new and hot topic of research.In this paper,based on the fractional-order calculus theory and the sliding mode theory,the synchronization of a class of fractional-order nonlinear time-delay systems is studied.The synchronization method is verified by the Lyapunov stability theorem and the stability of the fractional system.At the same time,this synchronization method is applied in secure communication.The main content of this paper are as follows:Firstly,the time domain model of fractional-order nonlinear systems is transformed into frequency domain model,a new fractional-order terminal sliding surface is designed based on the terminal sliding mode control theory and the stability of the sliding surface is verified.What's more,a dynamic sliding mode synchronous controller is designed for the system with external disturbance and uncertainty which can make the error system stable in the finite-time.The Lyapunov indirect method is used to prove the theory and finally calculate the synchronization time.Finally,the comparison of numerical simulation shows that the time of the designed controller making the control error system reach stable state is shorter than that of the ordinary sliding mode controller and the designed controller can effectively suppress chattering.Secondly,Aiming at the synchronization problem of fractional-order nonlinear time-delay systems,a single fractional adaptive sliding mode controller for fractional ordernonlinear time-delay systems is designed without eliminating nonlinear terms.Under the effect of this controller,the controlled error system gradually stability.Numerical simulation realizes the synchronous control of fractional-order nonlinear time-delay systems.The theory and simulation results show that the proposed controller effectively eliminates the adverse effects of time delay on system.Compared with other controllers,the controller is more concise,lower control cost and better robustness.Finally,an adaptive fractional-order sliding mode controller is designed based on adaptive control method and terminal sliding mode control theory for the system synchronization problem of the fractional-order nonlinear time-delay chaotic systems when the boundary of external interference and uncertainty is unknown.Combined with practical applications,the proposed theory is applied to secure communication.Through Matlab simulation,the results said that not only the feasibility and effectiveness of the adaptive fractional-order sliding mode controller,but also the successful combination of theory and secure communication.