Study On The Time-delayed Feedback Control Of Chua's Circuit Chaotic System

Chua's circuit is a typical chaotic circuit which has wild applications in electronic communication field and good values for research. In this paper, Chua's circuit chaotic system is the main study object. We analyzed the dynamic behaviors and the time-delayed state feedback control of Chua's circuit chaotic system. The main research contents are as follows:(1) We have analyzed chaotic dynamics and stability of equilibrium point of Chua's circuit chaotic system. Based on the theory of Hopf bifurcation of time-delayed system, a single delayed state feedback controller is designed to control the chaotic motion of the Chua's circuit system. First, the stability of the equilibriums and the chaotic motion of Chua's circuit system are investigated. Then, the necessary controllable ranges of the feedback gains are determined via detailed analysis for each of the x, y, z single delayed state feedbacks, respectively. Finally, the results of numerical simulation verify the validity of the theoretical analysis.(2) Based on the single delayed state feedback control, we proposed the full-states feedback control idea. This method enhanced the control effectiveness well. Utilizing the resultant theory and computer algebra, we can determine the controlled conditions under delayed feedback control. It's also means the analytic relationship between delayed timeτand feedback gains k .We can get the bifurcation diagram of target periodic orbit for the control parameters. At last, we have controled the motion of Chua's circuit chaotic system to different periodic orbits with different control parameters.(3) We have researched the tracking control problems of continuous chaotic system under delayed state feedback .At the same time, we given out the model of controlled system. According to Lyapunov stability theory, we proved the feasibility of assuage the chaotic motion to periodic orbit through time-delayed feedback control. On the basis of automatic adjustment gradient descent theory, we can get the way to determine the period values of unstable periodic orbits and the feedback gain. Finally, selecting the period value of target unstable periodic orbit and the corresponding feedback gain, the relevant control effects of tracking unstable periodic orbits have been given.