Recursive algorithms for inner ellipsoidal approximation of convex polytopes |
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Authors: | Fabrizio Dabbene [Author Vitae] Paolo Gay [Author Vitae] |
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Affiliation: | a IEIIT-CNR, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy b Dipartimento di Economia e Ingegneria Agraria, Forestale e Ambientale, Università degli Studi di Torino, Grugliasco (To), Italy c Institute for Control Science, Moscow, Russia |
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Abstract: | In this paper, fast recursive algorithms for the approximation of an n-dimensional convex polytope by means of an inscribed ellipsoid are presented. These algorithms consider at each step a single inequality describing the polytope and, under mild assumptions, they are guaranteed to converge in a finite number of steps. For their recursive nature, the proposed algorithms are better suited to treat a quite large number of constraints than standard off-line solutions, and have their natural application to problems where the set of constraints is iteratively updated, as on-line estimation problems, nonlinear convex optimization procedures and set membership identification. |
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Keywords: | Estimation Ellipsoidal approximation Convex polytope |
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