Stabilizing unstable periodic orbits of chaotic systems with unknown parameters

A novel adaptive time-delayed control method is proposed for stabilizing in herent unstable periodic orbits (UPOs) in chaotic systems with unknown para meters. We first explore the inherent properties of chaotic systems and use the system state and time-delayed system state to form an asymptotically s table invariant manifold so that when the system state enters the manifold and stays in it thereafter, the resulting motion enables the stabilization of the desired UPOs. We then use the model following concept to construct a n identifier for the estimation of the uncertain system parameters. We shal l prove that under the developed scheme, the system parameter estimates wil l converge to their true values. The effectiveness of the method is confirm ed by computer simulations.