In this talk we consider the problem of decentralized control of linearsystems. We employ the theory of partially ordered sets to model and analyzea class of decentralized control problems. Posets have attractivecombinatorial and algebraic properties; the combinatorial structure enablesus to model a rich class of communication structures in systems, and thealgebraic structure allows us to reparametrize optimal control problems toconvex problems. Building on this approach, we develop a state-spacesolution to the problem of designing $mathcal{H}_2$-optimal controllers.Our solution is based on the exploitation of a key separability property ofthe problem that enables an efficient computation of the optimal controller bysolving a small number of uncoupled standard Riccati equations. Our approachgives important insight into the structure of optimal controllers, such ascontroller degree bounds that depend on the structure of the poset. A novelelement in our state-space characterization of the controller is a pair oftransfer functions, that belong to the incidence algebra of the poset, areinverses of each other, and are intimately related to estimation of thestate along the different paths in the poset.
Joint work with Pablo Parrilo.
BIO:
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Parikshit Shah is a PhD candidate in the Department of ElectricalEngineering and Computer Science at MIT. He received his SM from StanfordUniversity in 2005 and his B.Tech. from the Indian Institute of Technology,Bombay in 2003.