Self-locating control of chaotic systems using Newton algorithm

An algorithm is introduced, based on the Newton method, to stabilize chaotic systems onto a desired periodic orbit utilizing the feedback of an output sequence on accessible parameters. The method does not necessarily rely on explicit knowledge of the system dynamics and only an approximate location of the desired periodic orbit is required which can subsequently be automatically and accurately detected in the control process. The algorithm is locally stable, has a fast convergence rate, is applicable to arbitrary dimensional systems, and is suitable for experimental situations. In numerical simulations, a pair of periodically forced, coupled Duffing oscillators is investigated, which produce a 4-D system.