Study On Control And Synchronization Methods Of Continuous Chaotic System

Chaos is an extremely complex common phenomenon which is generatedby a deterministic nonlinear system. It appears everywhere both in the natureand society. Since chaos has mach strange character such as "butterfly effect",it is the hot topic and the difficult problem to depress the harmful chaos andintroduce favorable chaos. Based on the existed results, studies on the controland synchronization of continuous-time chaotic system are carried out. Themain works are listed as follows:Firstly, the variable structure control theory is applied for the problem of aclass of chaotic system with unknown parameters. It is designed combined withadaptive control method to realize the parameter identification and the systemcontrol simultaneously. The parameter identification is realized in the closedloop, and the system is stabilized at the equilibrium point.Secondly, the lag synchronization problem is considered for a class ofLipschtiz nonlinear chaotic system based on sliding mode observer design. Twocases are discussed for the Lipschitz constant. When the Lipschitz constant isunknown, the design problem is solved with adaptive control method. At thesame time, the application in secure communication of the synchronizationmethod is initially considered.Thirdly, a novel synchronization method: dynamic surface control (DSC)method is proposed to improve the performance of backstepping method.Synchronization controllers of the R?ssler system are designed respectively fortwo cases of the system parameters: known and unknown. Furthermore, theDSC method is applied to a more general chaotic system: Lorenz system. Forthe introduction of a first-order filter, this synchronization method overcomesthe problem of "explosion of complexity" in backstepping method, and thedesigned controller is much simpler and more feasible.Lastly, the problems of impulsive control and synchronization of chaoticsystem are considered. On the condition that there exists delay in the systemoutput, the impulsive control theory and the T-S fuzzy model are applied tohelp controller design for delay or non-delay chaotic systems. A novel methodfor impulsive chaos synchronization in the presence of transmit channel delayis offered. Besides, we realize the impulsive generalized synchronization ofdelay chaotic system based on nonlinear delay impulsive differential equationstability theory. All the designs are proposed after thoroughly considering theeffects of the output and channel delays, so the method has more practicalsignificance.