Research On Control Strategy Of New Fractional Order Chaotic System

Fractional chaotic system is more complex than that of integer chaos system.It has become a hotspot of chaos research instead of integer chaos system because of its more extensive description of the scope and more broad application prospects.At the same time,the control and synchronization of fractional chaotic systems have become a hot academic topic in chaos.In the background of the study of fractional chaos system,the decision and control method of fractional chaotic system are studied and discussed in this paper.The main contents and results are as follows:Firstly,the properties of fractional Caputo derivative functions are deduced and proved according to the basic theory of fractional order.The Caputo fractional derivative is used as a tool to solve the fractional nonlinear differential equation in this paper,and the differential transformation method is used as a means at the same time to solve the fractional order nonlinear equation.On this basis,the generalized differential transform method is improved and the MDTM(modified differential transform method)is deduced The feasibility and accuracy of the method for solving fractional equations are deduced and verified and the adaptive control of fractional chaotic system is realized combining fractional nonlinear system stability theory.The effectiveness of the control method is verified.Secondly,the dynamic analysis of a new fractional chaotic system is carried out according to the basic theory of chaos.The method of judging chaos is optimized in this paper.It uses the "0-1" test method to test system chaos.This means is more efficient and effective.The superiority of the control method is verified by numerical simulation.Finally,the unknown parameters of the fractional chaotic system are identified under the adaptive rules and controller,meanwhile,the driving system and the response system are simulated to track the state vector error toward to zero asymptotically.At the same time,the unknown parameters of the system are extended to the unsteady function,and the adaptive control of the fractional chaotic system and the identification of unknown parameters are also realized.A faster control speed and a wider application space of this control method are verified by the Simulink simulation.