The Effectiveness Study Of A Type Of Chaos Control And Synchronization

Chaos is very interesting nonlinear phenomenon .It is found to be useful or has great potential. Chaos control and synchronization have become a useful and important topic.This paper focuses on the chaotic systems and its control, aimed at achieving chaos control and synchronization fast.Firstly,we analyze systemically the history and international actualities of the research,and we formulate the basic theory of chaos dynamics.Secondly,the chaotic control of LFRBM's system is studied by means of linear feedback method and coordinate transformation for the system's parameters known or unknown in advance.When the parameters are known.the variation range of feedback is shown;when the parameters are unknown,an adaptive controller is designed,with which the control parameters can be adjusted automatically.It is proved by using Lyapunov function that the controlled system can be asymptotically stabilized to five equilibriums with the controller.The simulation results vertify the effectiveness of proposed methods .Thirdly, Chen's chaotic system is controlled successfully by means of some feedback methods ,such as linear feedback, nonlinear feedback, differential feedback, delayed feedback etc. By theoretical analysis and simulation experiments, the effectiveness of our proposed methods is vertified, the variation range of feedback gain k is showed.Fourthly, the chaos system is controlled to any desired smooth orbit at an exponent rate by multi-dimensional variable tracking control.The Elwakil chaotic system is considered as an example.and Elwakil chaotic system is controlled to equilibra or cycle.and both the self synchronization and the synchronization with Rossler's chaotic system are discussed as well.The form of the controller is simple.the speed is quick.and the applicative range is extensive.In the end,computer simulations illustrate the effectiveness of the proposed method.Finally,an optimal control strategy that directs a kind of chaotic motion to any desired fixed point is proposed by using Ballman's Dynamic Programming and optimal control theory. Chua chaotic system and Rucklidge chaotic system are treated as examples, the simulation results vertify the effectiveness of our proposed method .