Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay

We propose a simple adaptive delayed feedback control algorithm for stabilization of unstable periodic orbits with unknown periods. The state dependent time delay is varied continuously towards the period of controlled orbit according to a gradient-descent method realized through three simple ordinary differential equations. We demonstrate the efficiency of the algorithm with the Rossler and Mackey-Glass chaotic systems. The stability of the controlled orbits is proven by computation of the Lyapunov exponents of linearized equations. (C) 2011 Elsevier B.V. All rights reserved.