Opf Control of Chaotic Systems | Analytical and Simulation Results

In this paper we present some theoretical results of the possibilities for controlling a given chaotic system using the (occasional proportional feedback) OPF method. It is usually claimed that the OPF method can be used only if the return map is almost one{dimensional and that the OPF control lacks a theoretical background for the choice of the feedback gain. We show how to nd the gain value for which the stabilization can be obtained. We prove that the possibility of stabilization depends on the behavior of the system in the neighborhood of the periodic orbit and not on the dimensionality of the attractor on the Poincar e surface.