Stabilizing unstable periodic orbits in large stability domains with dynamic time-delayed feedback control

Abstract

Dynamic time-delayed feedback control (DDFC) is applied to stabilize the unstable periodic orbits (UPOs) of chaotic systems in large stability domains. The stability domain is defined as certain areas of the parameter space of the feedback strength, in which the UPOs are stabilized. The control effect of the DDFC with a second-order controller system is investigated by considering two control objectives: to broaden the stability domain of the controlled UPOs and to minimize the modulus of the largest Floquet multiplier, which leads to a multi-objective optimization problem (MOP). The MOP is solved with the genetic algorithm. Case studies indicate that the control effect of the DDFC is significantly better than that of original time-delayed feedback control. The DDFC can stabilize the UPOs in a large stability domain and with a small modulus of the largest Floquet multiplier when the adjustable parameters of the controller system are properly designed.