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GRASP Special Seminar – Parikshit Shah, Massachusetts Institute of Technology, “A Partial Order Approach to Decentralized Control”

January 26, 2011 @ 1:00 pm - 2:00 pm

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.


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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.


January 26, 2011
1:00 pm - 2:00 pm
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