Control of chaotic systems using targeting by extended control regions method

In this work, the previously proposed extended control regions (ECR) algorithm for targeting is improved by using individual neural networks for each activation region. The improved version, which exploits the short time predictability of the chaotic system more efficiently, gives better performance with respect to training time and average reaching time while maintaining the advantages of the previous method. Moreover, the simulation results revealed that the meaningful number of activation regions of the controller using improved ECR is nearly linearly related with the prediction horizon of the chaotic system to be targeted, which can be used as a criterion for choosing the number of activation region.     

Targeting in dissipative chaotic systems: A survey

The large number of unstable equilibrium modes embedded in the strange attractor of dissipative chaotic systems usually presents a sufficiently rich repertoire for the choice of the desirable motion as a target. Once the system is close enough to the chosen target local stabilization techniques can be employed to capture the system within the desired motion. The ergodic behavior of chaotic systems on their strange attractors guarantees that the system will eventually visit a close neighborhood of the target. However, for arbitrary initial conditions within the basin of attraction of the strange attractor the waiting time for such a visit may be intolerably long. In order to reduce the long waiting time it usually becomes indispensable to employ an appropriate method of targeting, which refers to the task of steering the system toward the close neighborhood of the target. This paper provides a survey of targeting methods proposed in the literature for dissipative chaotic systems. (c) 2002 American Institute of Physics.