Synchronization And Application Of Fractional Order Chaotic System

Chaos is an important branch of nonlinear dynamics and a highly complex nonlinear system.Chaotic system has the basic characteristics of randomness,initial value sensitivity and irregular order,so it is widely used in geomagnetism,finance,power electronics and other fields.In recent years,scholars have introduced fractional calculus theory into chaos theory,which makes fractional order chaotic system have outstanding advantages in the study of chaos synchronization.Fractional order chaotic synchronization can increase the security of communication,which has aroused great interest in the field of image encryption.Therefore,it is of great significance to study fractional order chaos synchronization and its application.The main work and innovation of this paper are as follows:1.Considering the uncertainty and external disturbance of chaotic system in practical application,the combined synchronization of multiple fractional order chaotic systems is studied,and a new fractional order adaptive sliding mode controller is designed by combining sliding mode control and adaptive control method.Based on Lyapunov theory and fractional barbarat lemma,the stability of the controlled system is analyzed.The combined synchronization method extends the synchronization of single fractional order drive system and single fractional order response system,and has certain universality.The design of the controller takes into account the dual effects of uncertainties and external disturbances,and has a certain robustness.By selecting two groups of examples for simulation,the simulation results further show the feasibility of the controller.2.Combining adaptive control and predictive feedback control,a new adaptive predictive control method for fractional order chaos synchronization is proposed.By using the fractional Lyapunov stability theory,some new sufficient conditions for the synchronization of fractional order chaotic systems are derived.Compared with the existing results,this method does not need prior knowledge of feedback gain,and has fast convergence speed and is easy to implement in experiments.The effectiveness of the control method is verified by simulation with MATLAB.3.Aiming at the synchronization of fractional order chaotic systems with uncertainties and external disturbances,a new adaptive predictive sliding mode control method is proposed by combining sliding mode control and adaptive predictive control.By using the fractional Lyapunov stability theory,some new sufficient conditions for the synchronization of fractional order chaotic systems are derived.Numerical simulation further verifies the effectiveness of the control method4.Based on the adaptive predictive sliding mode synchronization scheme of uncertain fractional Chua chaotic system proposed in this paper,firstly,the digital image is encrypted by using the chaotic sequence output from the fractional Chua chaotic system as the driving system,and then the digital image is decrypted by using the synchronous chaotic sequence output from the uncertain fractional Chua chaotic system as the response system,so as to realize the secure communication of digital image.The designed encryption algorithm is related to plaintext,which increases the complexity of the algorithm.Therefore,the algorithm has better confidentiality and security for digital communication.