An adaptive delayed feedback control method for stabilizing chaotic time-delayed systems

This paper addresses a new adaptive delayed feedback control technique for stabilizing a class of chaotic time-delayed systems with a variable parameter. In the proposed scheme, the feedback gain of a delayed feedback controller is automatically tuned according to an adaptation law in order to stabilize unstable fixed points of the system. Such a mechanism provides a way to cope with unexpected changes in the parameters of the system. The adaptation algorithm is constructed based on the Lyapunov-Krasovskii's stability theorem. The control technique provides the advantages of increased stability and optimality, adaptability to the changes in the parameters, high privacy, simplicity, and noninvasiveness. The effectiveness of the control scheme is demonstrated using numerical simulations for a well-known chaotic time-delayed system.