Adaptive stabilization of unstable periodic orbits of chaotic systems

An adaptive time-delayed control method is proposed for stabilizing inherent unstable periodic orbits (UPOs) in chaotic systems. We first formulate the UPO stabilizing problem as a nonlinear optimal control problem, the analytic solution to which results in a controller stabilizing the desired UPOs. We then use the synchronization concept to construct an identifier for the estimation of the uncertain system parameters. We prove that under the developed scheme, the system parameter estimates will converge to their true values.