Invariance Entropy for Control Systems

  • For continuous time control systems, this paper introduces invariance entropy as a measure for the amount of information necessary to achieve invariance of weakly invariant compact subsets of the state space. Upper and lower bounds are derived, in particular, finiteness is proven. For linear control systems with compact control range, the invariance entropy is given by the sum of the real parts of the unstable eigenvalues of the uncontrolled system. A characterization via covers and corresponding feedbacks is provided.

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Metadaten
Author:Fritz ColoniusORCiDGND, Christoph KawanGND
URN:urn:nbn:de:bvb:384-opus4-10388
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1210
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2008-35)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Release Date:2008/12/09
Tag:nonlinear control; invariance; topological entropy; invariant covering
GND-Keyword:Topologische Entropie; Nichtlineare Kontrolltheorie; Invarianz
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehr- und Forschungseinheit Angewandte Analysis
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik