A Feedback Chaos Controller: Theory and Implementation

Zbigniew Galias1, Colm A. Murphy2, Michael Peter Kennedy3 and Maciej J. Ogorza lek1 1 Department of Electrical Engineering, University of Mining and Metallurgy, al. Mickiewicza 30, 30-059 Krak ow, Poland 2 Silicon and Software Systems, Ballymoss Rd., Sandyford Industrial Estate, Dublin 18, Ireland 3 Department of Electronic and Electrical Engineering, University College, Dublin 4, Ireland ABSTRACT The occasional proportional feedback (OPF) controller introduced by Hunt [1] for stabilizing periodic solutions in an autonomous chaotic system has the disadvantage that it requires an external synchronizing signal. In this paper we describe a modi ed version of Hunt's controller which obviates the need for an external synchronizing signal. We show how the controller has been used successfully to remove chaos in the chaotic Colpitts oscillator. We also describe some theoretical results on the possibilities for controlling a given chaotic system using the OPF method. 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.