Mems and nano devices such as micromechanisms that can swim, crawl, .y, autonomous micromanufacturing plants, microrobotic arrays, and next generation data storage, retrieval and search devices, will all constitute of large arrays (perhaps millions or more) of dynamic elements operating in unison. In essence these arrays, due to their autonomous features, adaptability to varying environmental conditions, and their own complex dynamics, will qualify to be called arti.cial organisms. Empowering them with autonomous control features will be a necessary task which will be quite di.erent from any of the control design problems encountered today. This proposal addresses the problem of designing controllers for such systems. It is argued that pattern formation is the key to controlling these systems. In contrast to simple electrical engineering circuitry, all organisms seem to be capable of (a) producing a large number of di.erent patterns, and in addition (b) capable of fast and graceful transition from one pattern to another. Control methodology sought after here will be mindful of these requirements. The question of what are appropriate patterns has for the most part been already addressed by biologists, physicists and mathematicians. However, there are two associated control challenges; (a) embedding such an equation in the natural dynamics of a mems or a nano array, and (b) how to design a control system to ensure quick and graceful transition from one pattern to another. Both these aspects are almost completely unexplored, and will be the focus of this research project. Among our interests will be (i) formulating and analyzing appropriate pole placement type problems, (ii) develop theories to understand how to design switching control laws that will minimize transient excursions, (iii) enumerate basic building blocks to create dynamic patterns, and .nding ways to (nonlinearly) superimpose them in order to generate complex dynamic patterns, (iv) formulate and solve appropriate model matching problems that arise in embedding pattern forming equations in microacuator/sensor arrays, and (v) asymptotically (at least practically asymptotically) stabilize dynamic patterns. Intellectual Merits Proposed research will lead to new classes of generic nonlinear control problems, and hence will impact upon the theory of nonlinear control in general. As far as we are aware, applicable mathematical theories discussed in the proposal have not previously been adapted to control theory. Seemingly these theories are at the very foundation necessary to understand how to control engineering actuator arrays of the future. Broader Impacts Micro- and nano- actuators are anticipated to play central roles in application areas such as microsurgery (mimic the hand movement of a surgeon in the micro scale), crawling, swimming and .ying robots performing tasks ranging from spying to drug delivery inside veins, audio processing devices that mimic the cochlear, and computing devices that mimic the brain functions. A concerted e.ort will be made to attract graduate and undergraduate students from under-represented groups, in particular from the large Hispanic community in the surrounding areas, to participate in the proposed research. We have already established a track record for supervising theses and dissertations of female students, and at least one female PhD student will receive partial funding from this grant. There is a very high probability that the theory to be developed will .nd a receptive application oriented and experimental oriented audience, due to our ongoing collaborations with the mems research group at the Maddox Laboratory at Texas Tech and the Texas Instruments Inc. through an NSF GOALI grant.
