Control And Synchronization Of Fractional-order Chaotic Systems

The origin of fractional calculus theory can be traced back to the 17 th century.Due to its wide application in the field of science and technology,fractional calculus theory has been fully developed in the 20 th century.On the other hand,as a unique dynamic form in nonlinear science,chaos has been widely concerned in the fields of mathematics,physics and bioengineering.As the core of chaos application,chaos control and chaos synchronization have become the focus of chaos research.The rise of fractional calculus theory expands the breadth and depth of chaos science,so the control and synchronization of fractional order chaotic system has become the most cutting-edge research hotspot in the 21 st century.However,due to the late start of the research on the control and synchronization of fractional order chaotic system,the related theories and technologies need to be further improved.This paper mainly studies the control and synchronization of fractional order chaotic systems.The main contents are as follows:In this paper,the dynamic properties of fractional order Zhang system and fractional order Hadi system are analyzed.Through numerical calculation,the parameter and order range of the two systems in chaotic state are obtained.It is found that two fractional order chaotic systems have different dynamic behaviors.The adaptive tracking control method is used to realize the tracking control of the fractional order Zhang system with unknown parameters.The effectiveness of the method is verified by theoretical analysis and numerical simulation.The adaptive finite time control method is used to realize the tracking control and unknown parameter identification of the fractional order Zhang system with unknown parameters.The theoretical analysis and numerical calculation verify the effectiveness of the method The effectiveness of the method is proved by adding external random disturbance.The projective synchronization method is used to study the synchronization of fractional order chaotic systems with different dimensions.Based on the projective synchronization theory,a suitable projective synchronization controller is designed.Taking the fractional order Zhang system and fractional order Hadi system as examples,the projective synchronization between fractional order chaotic systems with different dimensions is realized,and the numerical simulation is carried out with MATLAB.According to the circuit principle,the circuit model is established and the component parameters are determined.The simulation results of Multisim and MATLAB are compared,verifying their effectiveness.