Research On Algorithm Control Of Chaotic Time-delay Systems

The purpose of chaos control is to control the system in the unstable periodic orbit,and the chaos synchronization realizes the complete reconstruction of the chaotic state of the two systems.As a special pattern in nonlinear system,chaos has great sensitivity to initial value and noise.Therefore,the related research of chaotic system has great research value.This paper mainly studies from two aspects:For the stability problem of chaotic systems,there are still some conservatism in the existing theoretical results.In this paper,the stability and synchronization of the chaotic systems with time-delay are studied.In order to reduce the conservatism of the system,we construct new augmented Lyapunov-Krasovskii function.Meanwhile,we apply the Wirtinger-based inequality instead of the Jensen inequality to process the integral terms.Because the Wirtinger-based inequality considers the Jensen inequality as a special case,so it can effectively reduce the conservatism.At the same time,the alternate use of the first-order and second-order reciprocally convex combination can also obtain the smaller conservative stability conditions.The obtained stability condition is applied to the synchronization control of chaotic systems.In the study of synchronization for chaotic systems,we apply state feedback control and adaptive control to realize the synchronization of two chaotic systems.The state feedback method forms a closed loop system through the reaction of the feedback gain matrix to achieve the synchronization control.The adaptive control method continuously adjusts the parameters and states of the controller according to the state of the controlled system,so that the trajectories of two chaotic systems with different initial conditions are consistent with time.