Adaptive control of spatially extended systems: targeting spatiotemporal patterns and chaos

Abstract

We describe adaptive control algorithms whereby a spatially extended nonlinear system can be steered to a target state with desired spatiotemporal characteristics. Specifically we implement our control on a two-dimensional coupled map lattice, and successfully direct the system to desired targets ranging from spatiotemporal fixed points and regular spatial patterns to spatiotemporal chaos. The proposed methodology entails monitoring the local neighborhood of only one (arbitrary) site in order to regulate the entire lattice. Further, knowledge of the system's governing equations is not required. We also demonstrate the success of this method in controlling an unstable elastic array, a system of interest in engineering applications.