Invariance entropy for control systems [Elektronische Ressource] / von Christoph Kawan

Invariance entropy for control systems [Elektronische Ressource] / von Christoph Kawan

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Invariance Entropy for Control SystemsPromotionsschrift vonChristoph KawanInstitut fu¨r MathematikUniversit¨at Augsburg86135 Augsburgeingereicht bei derMathematisch-Naturwissenschaftlichen Fakulta¨tder Universita¨t AugsburgMai 2009Erstgutachter: Prof. Dr. Fritz Colonius, Universit¨at AugsburgZweitgutachter: Prof. Dr. Uwe Helmke, Universita¨t Wu¨rzburgTag der mu¨ndlichen Pru¨fung: 17. November 2009To Wolfi, Markus, and Eva-MariaContentsIntroduction 31 Control Theory 111.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2 Basics of Control Systems . . . . . . . . . . . . . . . . . . . . . . 181.3 Qualitative Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 452 Basics of Invariance Entropy 492.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.2 Elementary Properties . . . . . . . . . . . . . . . . . . . . . . . . 582.3 Isolated Sets and Inner Control Sets . . . . . . . . . . . . . . . . 663 Estimates 733.1 Upper Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.2 Lower Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834 Relation to Lyapunov Exponents 934.1 Linear and Inhomogeneous Bilinear Systems . . . . . . . . . . . . 944.2 Control Sets of Control-Affine Systems . . . . . . . . . . . . . . . 1125 Alternative Characterization, Data Rates and Numerics 1315.1 Characterization via Invariant Coverings . . . . . . . . . . . . . . 1315.

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Published 01 January 2009
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