A relationship between the prediction horizon and targeting in the control of chaotic systems

The control of chaotic systems based on the local stabilisation of a selected target, i.e. unstable equilibrium point or periodic orbit, usually requires the rapid steering of the system to a close neighbourhood of the target from an arbitrary initial point. This problem is referred to as a targeting problem in the literature. A previously proposed targeting method (1999), called an extended control regions (ECR) method, has been shown to provide a good performance allowing targeting action over a wider range of the phase space. The width of this range is directly related to the number of activation regions employed in the ECR method. The purpose of this paper is to demonstrate the relationship between the optimal number of activation regions to be employed in the ECR method and the prediction horizon of the chaotic system under investigation. This relationship provides a criterion for the selection of the number of activation regions in the ECR-based targeting