Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces:
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-27140 Inhaltsverzeichnis |
| Physical Description: | 115 S. |
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| adam_text | INVARIANCE ENTROPY FOR CONTROL SYSTEMS
ON LIE GROUPS AND HOMOGENEOUS SPACES
PROMOTIONSSCHRIFT VON
ADRIANO JOAO DA SILVA
INSTITUT FUR MATHEMATIK
UNIVERSITAT AUGSBURG
86159 AUGSBURG
DISSERTATION
ZUR ERLANGUNG DES DOKTORGRADES
DER MATHEMATISCH-NATURWISSENSCHAFTLICHEN FAKULTAT
DER UNIVERSITAT AUGSBURG
UND DER UNIVERSIDADE ESTADUAL DE CAMPINAS
DEZEMBER 2013
AUCH ONLINE VERFIIGBAR
HTTP://D-NB.INFO/105430520X
CONTENTS
INTRODUCTION 1
1 CONTROL SYSTEMS AND INVARIANCE ENTROPY 5
1.1 CONTROL SYSTEMS 5
1.2 INVARIANCE ENTROPY 10
1.2.1 DEFINITIONS AND BASIC PROPERTIES 10
1.2.2 UPPER AND LOWER BOUNDS FOR CONTROL-AFFINE SYSTEMS . 14
2 CONTROL SETS AND MORSE SETS AND THEIR FLAG TYPE 23
2.1 SEMI-SIMPLE THEORY 23
2.2 CONTROL SETS FOR SEMIGROUPS ACTIONS 28
2.3 MORSE DECOMPOSITION AND FLAG TYPE OF FLOWS 32
2.3.1 FLAG TYPE OF SEMIGROUPS OF AUTOMOPHISMS 33
2.3.2 FLAG TYPE FOR THE MORSE DECOMPOSITION OF FLOWS .... 34
2.4 IWASAWA DECOMPOSITION AND A-COCYCLE 37
3 THE FLAG CASE 45
3.1 HYPERBOLIC AFFINE SYSTEMS ON FLAG MANIFOLDS 45
3.2 ESCAPE ENTROPY AND LOWER BOUNDS ON FLAG MANIFOLDS 53
3.3 UPPER BOUND ON HYPERBOLIC CHAIN CONTROL SETS 59
4 LINEAR SYSTEMS ON LIE GROUPS 63
4.1 LINEAR SYSTEMS 63
4.1.1 QUASI-INVARIANT MEASURES 69
4.1.2 STABLE AND UNSTABLE LIE ALGEBRAS 74
4.2 LINEAR SYSTEMS ON HOMOGENEOUS SPACES 76
4.2.1 THE SEMI-SIMPLE CASE 82
1
5 INVARIANCE ENTROPY FOR RANDOM CONTROL SYSTEMS 85
5.1 PRELIMINARIES 85
5.2 DEFINITION AND ELEMENTARY PROPERTIES 89
5.3 LOWER AND UPPER BOUNDS . . . 94
5.4 THE LINEAR CASE 104
2
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| spelling | Da Silva, Adriano João 1985- Verfasser (DE-588)105403690X aut Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces von Adriano João da Silva 2013 115 S. txt rdacontent n rdamedia nc rdacarrier Augsburg, Univ., Diss., 2013 Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Entropie (DE-588)4014894-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kontrolltheorie (DE-588)4032317-1 s Entropie (DE-588)4014894-4 s Lie-Gruppe (DE-588)4035695-4 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:384-opus4-27140 http://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/2714 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-27140 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027430175&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Da Silva, Adriano João 1985- Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces Lie-Gruppe (DE-588)4035695-4 gnd Kontrolltheorie (DE-588)4032317-1 gnd Entropie (DE-588)4014894-4 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4032317-1 (DE-588)4014894-4 (DE-588)4113937-9 |
| title | Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces |
| title_auth | Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces |
| title_exact_search | Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces |
| title_full | Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces von Adriano João da Silva |
| title_fullStr | Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces von Adriano João da Silva |
| title_full_unstemmed | Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces von Adriano João da Silva |
| title_short | Invariance Entropy for Control Systems on Lie Groups and Homogeneous Spaces |
| title_sort | invariance entropy for control systems on lie groups and homogeneous spaces |
| topic | Lie-Gruppe (DE-588)4035695-4 gnd Kontrolltheorie (DE-588)4032317-1 gnd Entropie (DE-588)4014894-4 gnd |
| topic_facet | Lie-Gruppe Kontrolltheorie Entropie Hochschulschrift |
| url | http://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/2714 https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-27140 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027430175&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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