A multi-dimensional scheme for controlling unstable periodic orbits in chaotic systems

The control of unstable periodic orbits (UPOs) in chaotic systems is herein investigated by applying a weighted sum of external periodic inputs. These inputs are drawn from a “generic” set of basis functions and used to stabilize different UPOs in a chaotic attractor. All parameters associated with this multi-dimensional control scheme are experimentally computed without a priori knowledge of the system, thus making it easily applicable to a wide variety of dynamical systems. The performance of this control scheme is illustrated with several well-established chaotic systems.