Research On Synchronization Control Of Fractional-order Chaotic Systems With The Mixed Uncertainties

As a key method to solve the problem that the chaotic system applied effectively in the aspects including secure communication,image encryption,neural network and economic forecasting,the chaotic synchronization control has gradually become an important topic.With the development of the fractional calculus theory,a fractional-order chaotic system was proposed by many scholars in recent years,which has all integer-order chaotic characteristics and the fractional-order features of memory and heredity.Meanwhile,the system uncertainties have a significant and non-ignorable impact on many actual control systems.Considering the source of the system uncertainties,there are two common categories:the reducible uncertainties and the irreducible uncertainties.However,the actual systems are commonly subject to the mixed uncertainties,namely,both the reducible uncertainties and the irreducible uncertainties.If the single uncertainty is concerned,the designed controller could become too optimistic or conservative.Therefore,the synchronization control of a fractional-order chaotic system with the mixed uncertainties is investigated in this paper.With the research steps including control strategy design,synchronization scheme study and application simulation,the main contents of the paper are as follows:(1)An observer-based robust adaptive control scheme is proposed for a class of fractional nonlinear systems in presence of the parametric uncertainties and the external disturbances.By introducing a continuous frequency distributed model and using linear matrix inequalities(LMIs),a sufficient condition for robust asymptotic stability of fractional-order nonlinear systems is given.An H_?adaptive observer is designed for the system states and parameters estimation.Numerical simulations further demonstrate that the proposed method is effective.(2)A robust adaptive synchronization scheme is proposed for an uncertain fractional-order chaotic system with the same structure and mixed uncertainties.Based on the fractional-order Lyapunov stability theory and the adaptive control theory,an adaptive controller design method is presented for the robust asymptotic stability of synchronization error system.The proposed controller can ensure that the chaotic system synchronization is realized and the parameters estimated values are obtained at the same time.Numerical simulation verifies the effectiveness of the proposed method.(3)An improved observer-based robust adaptive synchronization scheme is proposed for uncertain fractional-order chaotic systems with the different structure and mixed uncertainties.The synchronization control scheme is discussed separately when the response system is divided into the certain system and the uncertain system with parameter perturbation and external disturbance.The estimated values of unknown parameters and system states can be obtained at the same time.Finally,the simulation results are presented to confirm our proposed method.(4)For the issue that the synchronization control of a fractional-order chaotic system is applied to the aspect of secure communication,according to the synchronization control scheme proposed above,the robust secure communication system is designed by using two kinds of secure communication method in this paper.The simulation results are carried out by using MATLAB,which can further verify that the designed method is effective.