Research On Feedback Control Method Of Chaos In High-Dimensional Systems

Diversity of chaotic system decides diversity of control methods, a kind of method or mode is not expected to control chaos phenomenon in nature.This paper introduces two new chaotic systems with n=4 and n=5, discusses methods to control chaos in high-dimensional systems by linear feedback, delayed feedback, enhancing linear feedback and enhancing delayed feedback.The paper takes two chaotic systems as example to study linear feedback method to control chaos. The mechanism of linear feedback control for chaotic motion is analyzed by the Lyapunov method to get the state feedback control rule which makes chaotic system stabilize. Simulation results show the system can be controlled to stable state and periodic motion by choosing the feedback intensity properly.Delay feedback method to control four-dimensional system is studied by the analytical approaches. The paper gives general analytic condition of control parameters by using the conditions and methods of Hopf bifurcation of delay system. The unstable orbits of the system can be stabilized under the conditions from the analytic analysis through numerical calculation.Based on controlling high-dimensional chaotic systems by the linear feedback and delay feedback, two corresponding enhancing projects are proposed for practical application by adding the number of feedback variable. Enhancing linear feedback in the hyper jerk system with n=5 is studied, the state feedback control rule is gotten. Analysis research of controlling chaotic system by enhancing delayed feedback gives analytic conditions for the four-dimensional continuous chaotic system theoretically. Applying two conclusions to practical systems, it is shown that the quality of control can be improved obviously.The theoretical description and numerical calculation indicate that these four methods can control the chaotic motion in high-dimensional systems to the desired target orbit, the effectiveness and feasibility of the methods are illustrated.The research in the Paper provides theoretical and experimental foundation for the control of chaos in high-dimensional systems and has certain guiding significance.