Directing orbits of chaotic systems in the presence of noise: Feedback correction

In this paper, we consider the directing of orbits of chaotic dynamical systems towards desired targets in the presence of random dynamical noise. Our aim is to significantly reduce the time needed to reach a target region by applying only small, bounded perturbations. We outline a technique for deriving open-loop controllers based on optimal control theory, and then propose methods for improving the performance of these controllers to counter the effects of noise. The improvements are illustrated by examples.