ADAPTIVE-CONTROL OF SPATIALLY EXTENDED SYSTEMS - TARGETING SPATIOTEMPORAL PATTERNS AND CHAOS

We describe adaptive control algorithms whereby a spatially extended n onlinear system can be steered to a target state with desired spatiote mporal characteristics. Specifically we implement our control on a two -dimensional coupled map lattice, and successfully direct the system t o desired targets ranging from spatiotemporal fixed points and regular spatial patterns to spatiotemporal chaos. The proposed methodology en tails monitoring the local neighborhood of only one (arbitrary) site i n order to regulate the entire lattice. Further, knowledge of the syst em's governing equations is not required. We also demonstrate the succ ess of this method in controlling an unstable elastic array, a system of interest in engineering applications. [S1063-651X(98)51011-2].