On control of chaos: Higher periodic orbits

Abstract

In this paper, we consider control and simultaneous stabilization of chaotic dynamical systems onto higher periodic orbits. Our aim is to control chaos using local linear state, feedback control. After analysing the applicability of such a control, we present numerical techniques for constructing effective controllers. The control is achieved using small, bounded perturbations. We also give a sufficient condition for stabilizing control around higher periodic orbits. The methods proposed are shown to be effective for some examples even in the presence of relatively small random dynamical noise.