Synchronization Of Double Uncertain Fractional Order Chaotic System

The control and synchronization of fractional-order chaotic systems is one of the most interesting topics,which attract many researchers.Time lag,parameter perturbation,unknown functions,and external disturbances are complex factors and uncertain elements which often encountered in our real life and engineering applications.It is particularly important to effectively control and synchronize the fractional-order chaotic system to make the system run efficiently and stably.If only one of the uncertain factors in the system or outside the natural environment is considered in the design of the controller,it is too optimistic.And the research on the control algorithm of uncertain fractional-order systems is still in its infancy.Some control synchronization methods need to be further improved,which is also a challenge faced at the same time.Therefore,the fractional-order chaos model with internal uncertain parameters and external interference terms is more representative of the actual system.If we study it which is great value to human society and engineering applications.This paper focuses on a kind of subjective factors(unknown parameters,different orders,time delay)and dual uncertain fractional order chaotic system with external disturbance.A terminal sliding mode controller with a fractional sliding surface is used to control two fractional chaotic systems synchronously,which the problem of parameter uncertainty and external interference are solved.At the same time,stability is not only the basic performance requirement of the system,but also the main factor that is prioritized in the controller design process.However,using a single way of FSMC will introduce perturbation parameters which lead to chattering.In order to weaken chattering,adaptive fuzzy control is added to the initial designed controller.It will reduce the instability and improve the working efficiency of the controller in the actual project.The convergence of synchronization error is proved based on the theory of fractional order stability.This shows the feasibility and superiority which use fuzzy control to improve sliding mode control.Finally,it is proved that the method is effective through numerical simulation.