October 22, 2010, 1100 Webb

We consider a class of decentralized control problems that can be modeled in terms of partially ordered sets (posets). We provide a complete state-space solution to the problem of H2-optimal decentralized control (with state feedback) of poset-causal systems. We establish a technique to solve such problems by exploiting a certain separation property of the problem, and the incidence algebra of the poset. We show how to compute the optimal solution efficiently by solving a small number of Riccati Equations, establish degree bounds, and determine the structure of the optimal controller. This generalizes earlier work of Swigart and Lall, for the two- controller case. A key element in our analysis is a pair of transfer functions, inverses of each other, that are intimately related to the estimation structure in the optimal controller. Joint work with Parikshit Shah (MIT).

Pablo A. Parrilo received an Electronics Engineering undergraduate degree from the University of Buenos Aires, and a Ph.D. in Control and Dynamical Systems from the California Institute of Technology. He has held short-term visiting appointments at the University of California at Santa Barbara (Physics), Lund Institute of Technology (Automatic Control), and UC Berkeley (Mathematics). From October 2001 through September 2004, he was Assistant Professor of Analysis and Control Systems at the Automatic Control Laboratory of the Swiss Federal Institute of Technology (ETH Zurich). He is currently the Finmeccanica Career Development Professor of Engineering at the Department of Electrical Engineering and Computer Science of the Massachusetts Institute of Technology, where he is also affiliated with the Laboratory for Information and Decision Systems (LIDS) and the Operations Research Center (ORC). Professor Parrilo is the recipient of the 2005 Donald P. Eckman Award of the American Automatic Control Council, as well as the 2005 SIAM Activity Group on Control and Systems Theory (SIAG/CST) Prize. He was also a finalist for the Tucker Prize of the Mathematical Programming Society for the years 2000-2003. He is currently on the Board of Directors of the Foundations of Computational Mathematics (FoCM) society, and a member of the Editorial Board of the MOS/SIAM Book Series on Optimization. His research interests include optimization and game theory methods for engineering applications, control and identification of uncertain complex systems, robustness analysis and synthesis, and the development and application of computational tools based on convex optimization and algorithmic algebra to practically relevant engineering problems.