Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces

  • In this thesis we will analyse the invariance entropy of admissible pairs for control systems on Lie groups and homogeneous spaces. The main goal is to improve the known upper and lower bounds for such entropy and see when it is possible to prove that these bounds coincide, which give us an expression for the entropy. We will show that for induced control-affine systems on the flag manifolds both, the upper and lower bounds are given by the determinant of the unstable part of the system and they differ just on the set where we consider the infimum. For Linear systems on abelian, nilpotents and compact Lie groups we have an expression for the invariance entropy and in the semi-simple case, the upper and lower bounds equality depend on the exponential growth of an associated driftless control-affine system. At the end of the thesis we introduce a concept of entropy for random control systems and derive general bounds for it.

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Author:Adriano João da Silva
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Advisor:Fritz Colonius, Luiz A. B. San Martin
Type:Doctoral Thesis
Publishing Institution:Universität Augsburg
Granting Institution:Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät
Date of final exam:2014/02/28
Release Date:2014/06/02
Tag:control theory; invariance entropy; Lie groups; flag manifolds
GND-Keyword:Kontrolltheorie; Entropie; Lie-Gruppe
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand