Bilinear control systems: matrices in action
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht, Heidelberg, London, New York
Springer
2009
|
| Schriftenreihe: | Applied mathematical sciences
169 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | IX, 280 Seiten Illustrationen |
| ISBN: | 9781402096129 9781402096136 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | DAVID L. ELLIOTT BILINEAR CONTROL SYSTEMS MATRICES IN ACTION SPRINGER
CONTENTS 1 INTRODUCTION 1 1.1 MATRICES IN ACTION 2 1.2 STABILITY: LINEAR
DYNAMICS 7 1.3 LINEAR CONTROL SYSTEMS 8 1.4 WHAT IS A BILINEAR CONTROL
SYSTEM? 10 1.5 TRANSITION MATRICES 13 1.6 CONTROLLABILITY 20 1.7
STABILITY: NONLINEAR DYNAMICS 24 1.8 FROM CONTINUOUS TO DISCRETE 28 1.9
EXERCISES 30 2 SYMMETRIC SYSTEMS: LIE THEORY 33 2.1 INTRODUCTION 33 2.2
LIE ALGEBRAS 34 2.3 LIE GROUPS 44 2.4 ORBITS, TRANSITIVITY, AND LIE RANK
54 2.5 ALGEBRAIC GEOMETRY COMPUTATIONS 60 2.6 LOW-DIMENSIONAL EXAMPLES
68 2.7 GROUPS AND COSET SPACES 70 2.8 CANONICAL COORDINATES 72 2.9
CONSTRUCTING TRANSITION MATRICES 74 2.10 COMPLEX BILINEAR SYSTEMS 77
2.11 GENERIC GENERATION 79 2.12 EXERCISES 81 3 SYSTEMS WITH DRIFT 83 3.1
INTRODUCTION 83 3.2 STABILIZATION WITH CONSTANT CONTROL 85 3.3
CONTROLLABILITY 89 3.4 ACCESSIBILITY 100 3.5 SMALL CONTROLS 104 VII VIUE
CONTENTS 3.6 STABILIZATION BY STATE-DEPENDENT INPUTS 107 3.7 LIE
SEMIGROUPS 116 3.8 BIAFFINE SYSTEMS 119 3.9 EXERCISES 124 4
DISCRETE-TIME BILINEAR SYSTEMS 127 4.1 DYNAMICAL SYSTEMS: DISCRETE-TIME
128 4.2 DISCRETE-TIME CONTROL 129 4.3 STABILIZATION BY CONSTANT INPUTS
131 4.4 CONTROLLABILITY 132 4.5 A CAUTIONARY TALE 141 5 SYSTEMS WITH
OUTPUTS 143 5.1 COMPOSITIONS OF SYSTEMS 144 5.2 OBSERVABILITY 146 5.3
STATE OBSERVERS 151 5.4 IDENTIFICATION BY PARAMETER ESTIMATION 153 5.5
REALIZATION 154 5.6 VOLTERRA SERIES 161 5.7 APPROXIMATION WITH BILINEAR
SYSTEMS 163 6 EXAMPLES 165 6.1 POSITIVE BILINEAR SYSTEMS 165 6.2
COMPARTMENTAL MODELS 170 6.3 SWITCHING 172 6.4 PATH CONSTRUCTION AND
OPTIMIZATION 179 6.5 QUANTUM SYSTEMS 184 7 LINEARIZATION 187 7.1
EQUIVALENT DYNAMICAL SYSTEMS 188 7.2 LINEARIZATION: SEMISIMPLICITY AND
TRANSITIVITY 192 7.3 RELATED WORK 198 8 INPUT STRUCTURES 201 8.1
CONCATENATION AND MATRIX SEMIGROUPS 201 8.2 FORMAL POWER SERIES FOR
BILINEAR SYSTEMS 204 8.3 STOCHASTIC BILINEAR SYSTEMS 207 MATRIX ALGEBRA
215 A.L DEFINITIONS 215 A.2 ASSOCIATIVE MATRIX ALGEBRAS 217 A.3
KRONECKER PRODUCTS 220 A.4 INVARIANTS OF MATRIX PAIRS 223 CONTENTS IX
LIE ALGEBRAS AND GROUPS 225 B.L LIE ALGEBRAS 225 B.2 STRUCTURE OF LIE
ALGEBRAS 229 B.3 MAPPINGS AND MANIFOLDS 231 B.4 GROUPS 238 B.5 LIE
GROUPS 240 ALGEBRAIC GEOMETRY 247 C.L POLYNOMIALS 247 C.2 AFFINE
VARIETIES AND IDEALS 248 TRANSITIVE LIE ALGEBRAS 251 D.L INTRODUCTION
251 D.2 THE TRANSITIVE LIE ALGEBRAS 255 REFERENCES 259 INDEX 273
A control system is called bilinear
ifit
is described by linear differential equations in
which the control inputs appear as coefficients. The study of bilinear control systems
began in the
1960s
and has since developed into a fascinating field, vital for the
solution of many challenging practical control problems. Its methods and applications
cross inter-disciplinary boundaries, proving useful in areas as diverse as spin control
in quantum physics and the study of Lie semigroups.
The first half of the book, based upon matrix analysis, introduces Lie algebras,
controllability and stabilization. Individual chapters are dedicated to topics such
as discrete-time systems, observability and realization, examples from science and
engineering, linearization of nonlinear systems, and input-output analysis.
Written by one of the leading researchers in the field in a clear and comprehensible
manner and laden with proofs, exercises and
Mathematica
scripts, this involving
text will be a vital and thorough introduction to the subject for first-year graduate
students of control theory. It will also be of great value to academics and researchers
with an interest in matrix analysis, Lie algebra, and semigroups.
|
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| ctrlnum | (OCoLC)634828770 (DE-599)DNB991182073 |
| discipline | Mathematik |
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| id | DE-604.BV035571077 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:40:41Z |
| institution | BVB |
| isbn | 9781402096129 9781402096136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017626661 |
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| physical | IX, 280 Seiten Illustrationen |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Elliott, David L. 1932- (DE-588)138483302 aut Bilinear control systems matrices in action David L. Elliott Dordrecht, Heidelberg, London, New York Springer 2009 IX, 280 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 169 Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4020-9613-6 Applied mathematical sciences 169 (DE-604)BV000005274 169 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017626661&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017626661&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Elliott, David L. 1932- Bilinear control systems matrices in action Applied mathematical sciences Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4032317-1 |
| title | Bilinear control systems matrices in action |
| title_auth | Bilinear control systems matrices in action |
| title_exact_search | Bilinear control systems matrices in action |
| title_full | Bilinear control systems matrices in action David L. Elliott |
| title_fullStr | Bilinear control systems matrices in action David L. Elliott |
| title_full_unstemmed | Bilinear control systems matrices in action David L. Elliott |
| title_short | Bilinear control systems |
| title_sort | bilinear control systems matrices in action |
| title_sub | matrices in action |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017626661&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017626661&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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