Control of travelling pulses in MEMS arrays: numerical evidence of practical asymptotic stabilization

Control of large arrays of microactuators and sensors, are anticipated to be of much interest to the technological advances of tomorrow. Prominent among the requisite control tasks would be that of producing stable dynamic patterns. Here we address the problem of practical asymptotic stabilization of travelling pulses in a one dimensional array of microactuators. Solitons are used as models of travelling pulses. A method is described to embed descretized KdV equation in a microactuator array, and an essentially local feedback control scheme is developed, for the purpose of practical asymptotic stabilization of solitons. While no proofs of asymptotic stability are given, numerical evidence is presented to support the conjecture that the proposed control scheme is practically asymptotically stabilizing.