The Study On Chaos Synchronization Based On State Observer

The phenomenon of chaos is well known for their complex nonlinear system. It ischaracterized by a sensitive dependence of a system’s dynamical variables on the initialconditions. Because of the unpredictability and the instability, we think it is harmfulphenomena. In order to make it serve us, use and control of the chaos has became the keysection of the chaos research. With the put forward of chaos control and chaossynchronization theory the boom of people scholar research on chaos control andsynchronization was beginning.Now days, researchers have proposed wide variety of synchronization control methods,due to the different of the synchronization method and the controller, the difficulty ofimplementation is different,but most of these methods hard to apply to the practice. Therefore,design a simple and easily achieved controller is practical significance.In this paper, we have studied synchronization of chaotic system using the numericalsimulation, according to adaptive control theory and state observer. There are four parts in thispaper. Firstly it has systematically introduced the chaos theory, including an overview of basicresearch of chaos, chaos control, chaos synchronization; especially introduced the concept ofchaos synchronization and several common methods. In the second part, I introduced thenumerical simulation of chaos synchronization and state observer. Based on state observerand use the case of new three–dimensional autonomous chaos system, by designing stateobserver, the chaos system kept synchronization, numerical simulations are used to prove theeffectiveness of the proposed method. In the third part, I studied the chaotic system withcertain parameters synchronization based on state observer, use the Liu system and the unifiedchaotic system as a case, through the theoretical analysis and numerical simulation proof thismethod can be used for synchronization of chaotic system. And the numerical simulationresult of Liu system and the unified chaotic system have been given in the paper. In the lastpart, I studied the chaotic system with uncertain parameters synchronization based onadaptive state observer, use the Chua system and Arneodo system as the case, through thetheoretical analysis and numerical simulation proof this method can be used for synchronization of chaotic system. And the numerical simulation result of Chua system andArneodo system have been given in this paper.In this paper, I studied the chaotic system with certain parameters and uncertainparameters, I proposed adaptive state observer of the synchronization method, theoreticalanalysis and numerical simulation proof this method can be used for synchronization ofchaotic system. This method has good applicability and it can be applied to the practice. It hasvery broad application prospects.