Research On Synchronization Of Typical Chaotic Systems Based On Adaptive-impulsive Control

Since the first chaotic attractor has been found by E.N Lorenz, the broad prospectsof chaos has attracted the attention of many scholars,which promoted the developmentof chaos.What’s more, chaos control has become a hotspot in the field of nonlinearscience, where the chaos synchronization accounts for a large proportion. Lots ofresearches indicated that chaos synchronization has very extensive application prospectsin many fields. This paper lays emphasis on the research of chaos synchronization basedon the adaptive control and impulsive control.In recent years, a large number of scholars involved in the theory of the chaossynchronization, the relevant scientific literaturesare also proposed, including variedcontrol methods. This paper focused on some typical chaotic systems, discussed theproblem of chaos synchronization of many chaotic systems with delays or uncertaintiesby using the theory of Lyapunov stability, impulsive control and adaptive control.Moreover, adaptive-impulsive control method for synchronizationis proposed.Inaddition, relevant theoretical derivations and numerical simulations are given. The maincontributions of this paper are as follows:①In view of chaos synchronization of Lorenz-Stenflo(LS) hyperchaotic sysem,the synchronization is achieved by impulsive control method, and the criterion ofimpulsive synchronization is presented based on the Lyapunov stability theory andimpulsive control theory. To verify the effectiveness of this method, numericalsimulationsare given. This method has the characteristics of small control energy, fastconvergence and wide universality.Moreover, this method can also applied to mosttypical hyperchaotic systems.②This paper investigates the synchronization problems of three differenthyperchaoticsystems, synchronization between different hyperchaotic systems isachieved.By constructing the response system, synchronization problem are convertedinto the stability problem of the dynamic error system. What’s more, the stabilitycriterion of the dynamic error system is presented based on the Lyapunov stabilitytheory. Moreover, relevant adaptive law is provided to adjust the uncertain parameters.This approach has simple construction, and also can applied to most typicalhyperchaotic systems.③Synchronization of a class of continuous chaotic systems is investigated, two control methods are discussed based on the Lyapunov stability theory,which areadaptive control and adaptive-impulsive control, and corresponding theoretical analysisisalso presented. In addition, some numerical simulations are given to verify theeffectiveness of approaches. What’s more, by comparing the response curves of the twomethods, the characteristic of rapid convergence of adaptive-impulsive control isreflected.④In view of the synchronization of a class of delayed chaotic systems withuncertain parameters, the synchronization is achieved by using adaptive control andadaptive-impulsive control respectively.What’s more, corresponding theoretical analysisis represented, and relevant adaptive law is given to adjust the uncertain parameter.Toshow the effectiveness of two schemes, some numerical simulations are given. Finally,the merits and demerits of the two schemes are explained by comparing the tworesponse curves.