Optimization and Systems Theory Seminar
Friday, April 28, 2006, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Michael Rotkowitz
Automatic Control
Signals Sensors and Systems
Royal Institute of Technology (KTH)
SE-100 44 Stockholm, Sweden
E-mail: michael.rotkowitz@ee.kth.se

Tractable Problems in Optimal Decentralized Control

The synthesis of optimal decentralized controllers for complex systems is a longstanding open problem. Conventional controls analysis breaks down when multiple controllers have access to different information. In the general case, this problem is notoriously difficult, even when the plant and possible controllers are all LTI. It is shown that when a simple condition holds, the optimal decentralized control problem may be recast as a convex optimization problem. This condition unified the few previously identified tractable problems, and has elucidated many new ones. The implications for optimal control subject to sparsity constraints will be shown, as will those for interconnected systems subject to communication delays. We then discuss recent work which considers all of the causal stabilizing controllers for such systems. A new condition is introduced, under which we may similarly parameterize all of the stabilizing decentralized controllers, even if the plant or admissible controllers may be nonlinear time-varying. In addition to extending LTI results to NLTV, we further see how this recent result may allow this work to extend beyond the field of decentralized control, to all types of constrained control problems. These results all hinge on being able to show that certain constraints are invariant under a feedback map. Time permitting, we'll discuss some of the more technical aspects of this research which made these results possible, including the development of a topology for operators on extended spaces, a resulting not-so-small gain theorem, and a convergence theorem based on a weak notion of contractiveness.

Calendar of seminars
Last update: February 28, 2006 by Marie Lundin.