Some Recent Progress in Distributed Control

Professor P. S. Krishnaprasad
University of Maryland

There is growing interest in the technology and mathematics of distributed control. The advent of smart nodes combining sensors, actuators, local computation, and (wireless) communication poses an interesting mathematical problem on approximate diagonalization of plant matrices. Our answer (in joint work with George Kantor) is based on gradient flows on matrix groups.

The availability of arrays of closely spaced MEMS actuators poses interesting problems in the study of gradient flows on function spaces. We note examples in adaptive optics in the published work of Mikhail Vorontsov and his collaborators. We also discuss prospects for an approach (in joint work with Eric Justh) based on pattern formation with applications to the problem of controlling fields.