Targeting via region scheduling for the control of chaotic systems

Abstract

The local control method for chaotic dynamics as proposed by Ott, Grebogi and Yorke (the OGY method) has drawn the attention of many non-linear system researchers within the last decade. This method exploits the properties of chaotic dynamics for an acceptable control performance. The OGY method can stabilise a target, i.e. a chosen unstable equilibrium point or an unstable periodic orbit, without a priori knowledge about the system dynamics. In the literature there exist many extensions and modifications of this approach. The major drawback of these methods is the long waiting time, which is required the system converges to a close neighbourhood of the target since the control is based on a linearization around the target. In addition to the OGY method and its extensions, neural networks are also being utilised for the control of chaotic dynamics. The aim of this work is to achieve the stabilization of the target without priori knowledge about the system dynamics, while reducing the average time to reach the close neighbourhood. The local modelling of the dynamics is achieved using a neural networks employing Radial Basis Functions. A sufficient reduction in the reaching time and satisfactory stabilization of the desired target has been achived by this method.