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Pablo A. Parrilo. Shah, Parikshit (Parikshit Mayank) Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2011-10-17T21:28:51Z 2011-10-17T21:28:51Z 2011 2011 http://hdl.handle.net/1721.1/66462 756044032 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 173-177). In this thesis we consider the problem of decentralized control of linear systems. We employ the theory of partially ordered sets (posets) 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 H₂-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. We then view the control design problem from an architectural viewpoint. We propose a natural architecture for poset-causal controllers. In the process, we establish interesting connections between concepts from order theory such as Mobius inversion and control-theoretic concepts such as state estimation, innovation, and separability principles. Finally, we prove that the H₂-optimal controller in fact posseses the proposed controller structure, thereby proving the optimality of the architecture. by Parikshit Shah. Ph.D. 177 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. A partial order approach to decentralized control Thesis application/pdf Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="834d974f-5caa-49d8-929a-383590393cef"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>A partial order approach to decentralized control</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2011</PublicationDate> <Authors> <Author> <DisplayName>Shah, Parikshit (Parikshit Mayank)</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>In this thesis we consider the problem of decentralized control of linear systems. We employ the theory of partially ordered sets (posets) 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 H₂-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. We then view the control design problem from an architectural viewpoint. We propose a natural architecture for poset-causal controllers. In the process, we establish interesting connections between concepts from order theory such as Mobius inversion and control-theoretic concepts such as state estimation, innovation, and separability principles. Finally, we prove that the H₂-optimal controller in fact posseses the proposed controller structure, thereby proving the optimality of the architecture.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>