Passive Control Of Fractional Order Chaotic Systems

Chaos is an aperiodic motion form in nonlinear systems,which involves every branch of natural science and social science.Chaotic system has the characteristics of randomness,initial value sensitivity and irregularity,and is widely used in physics,communication,engineering and other fields.In recent years,with the development of computer technology,the study of chaos has become more in-depth.Scholars have discovered the advantages of fractional calculus theory in the application of chaos theory,which extends the order of chaos to the range of fractions and obtains the fractional-order chaos model.It has theoretical and practical value to study and realize the control and synchronization of fractional-order chaotic systems.In this paper,the control of fractional-order chaotic systems,asymptotic synchronization and finite time synchronization of error systems are studied,and passive backstepping controllers and adaptive passive backstepping controllers are designed.The main content and research results of this paper are as follows:1.A passive backstepping control method for fractional-order chaotic systems is proposed by combining backstepping control theory and passive control theory.Based on the fractional Lyapunov stability theory,using sufficient conditions of passive control and the design framework of backstepping control,energy function and virtual controller are designed separately for each subsystem,and finally the passive backstepping controller of the whole system is designed.Finally,theoretical analysis and numerical simulation are carried out,and the simulation results are compared with other methods to verify the superiority of the proposed method.2.Aiming at the control and synchronization of fractional-order chaotic systems with uncertain parameters,combined with backstepping control and passive control,based on the fractional Lyapunov stability theory,and estimated the parameters of the system online,the energy function of the subsystem,the adaptive virtual control law and the actual adaptive control law of the whole system are designed.The control of uncertain fractional-order chaotic system and synchronous adaptive passive backstepping control are realized.The feasibility and rationality of the method are proved by the simulation results.3.Based on backstepping control theory and passive control theory,a finite time synchronization control method for fractional-order Shimizu-Morioka chaotic system is proposed.Based on the fractional Lyapunov stability theory and finite time stability theory,sufficient conditions of passive control and recursive process of backstepping control are used.The energy function and virtual control law of the subsystem are designed independently,and then the actual control law of the whole system is designed to realize the finite time synchronization of fractional-order Shimizu-Morioka chaotic system.The effectiveness of the method is proved by the Experimental results.