STABILIZING UNSTABLE PERIODIC TRAJECTORIES OF CHAOTIC SYSTEMS WITH TIME-VARYING SWITCHING DELAYED FEEDBACK CONTROL

In order to improve the effect of the classical delayed feedback control in stabilizing the unstable periodic trajectory and expand the stability region, the time-varying switching strategy is used to modify the classical delayed feedback control, which leads to the method of time-varying switching delayed feedback control. The control signal of the time-varying switching delayed feedback control only exists in specific time intervals, and there is no control signal in other time intervals, which is different from the fixed control signal in the classical delayed feedback control. Through case studies, the specific performance of time-varying switching delayed feedback control in stabilizing unstable periodic trajectory is investigated. The maximum conditional Lyapunov exponent of the controlled periodic trajectory is calculated as a function of the feedback strength. The relationship between the stability region of the controlled periodic trajectory and the switching frequency is obtained. The results show that with the increase of switching frequency, the stable region of the controlled periodic trajectory changes non smoothly. The stability region of the time-varying switching delayed feedback control is significantly larger than that of the classical delayed feedback control when the switching frequency is properly selected. In the engineering practice of chaos control, the control signal is often constrained. To achieve the stable control of the target periodic trajectory, the controlled periodic trajectory needs to have a large enough stable region. Therefore, compared with the classical time-delay feedback control, the time-varying switching time-delay feedback control proposed in this paper has a wider application prospect.