GRASP Special Seminar - Parikshit Shah, Massachusetts Institute of Technology, "A Partial Order Approach to Decentralized Control"

Abstract: In this talk we consider the problem of decentralized control of linear systems. We employ the theory of partially ordered sets to model and analyze a class of decentralized control problems. Posets have attractive combinatorial and algebraic properties; the combinatorial structure enables us to model a rich class of communication structures in systems, and the algebraic structure allows us to reparametrize optimal control problems to convex problems. Building on this approach, we develop a state-space solution to the problem of designing $\mathcal{H}_2$-optimal controllers. Our solution is based on the exploitation of a key separability property of the problem that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our state-space characterization of the controller is a pair of transfer functions, that belong to the incidence algebra of the poset, are inverses of each other, and are intimately related to estimation of the state along the different paths in the poset.  Joint work with Pablo Parrilo.

Presenter's biography

Parikshit Shah is a PhD candidate in the Department of Electrical Engineering and Computer Science at MIT. He received his SM from Stanford University in 2005 and his B.Tech. from the Indian Institute of Technology, Bombay in 2003.