Pattern-forming systems for control of large arrays of actuators

We consider an approach for coordinating the activity of a large array of m icroactuators via diffusive (i.e., nearest-neighbor) coupling combined with reactive growth and decay, implemented via interconnection templates which have been artificially engineered into the system (for example, in colloca ted microelectronic circuitry, or through the formulation of active materia l layers). Such coupled systems can support interesting spatiotemporal patt erns, which in turn determine the actuation patterns. Generating such spati otemporal patterns typically involves stressing the interconnections by rai sing or lowering a parameter resulting in the crossing of stability thresho lds. The possibility of making such parametric adjustments via feedback on a slower timescale offers a solution to the problem of communicating effect ively within a large array: The communication is achieved through the inter connection template. The mathematics behind this idea leads us into the ric h domain of nonlinear partial differential equations (PDEs) with spatiotemp oral pattern solutions. We present a global nonlinear stability analysis th at applies to certain model pattern-forming systems. The nonlinear stabilit y analysis could serve as a starting point for control system design for sy stems containing large microactuator arrays.