On linear-quadratic optimal control and robustness of differential-algebraic systems:
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| Format: | Thesis Book |
| Language: | English |
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Berlin
Logos Verlag Berlin GmbH
[2015]
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| Online Access: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Physical Description: | xviii, 284 Seiten Diagramme 21 cm |
| ISBN: | 9783832541187 3832541187 |
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| 245 | 1 | 0 | |a On linear-quadratic optimal control and robustness of differential-algebraic systems |c von Dipl.-Math. Matthias Voigt |
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| 502 | |b Dissertation |c Otto-von-Guericke-Universität Magdeburg |d 2015 | ||
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| 653 | |a Algebro-Differentialgleichungen | ||
| 653 | |a Optimale und robuste Regelung | ||
| 653 | |a Störungstheorie von Matrizen | ||
| 653 | |a Numerische Methoden | ||
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CONTENTS
LIST OF FIGURES V
LIST OF TABLES VII
LIST OF ALGORITHMS IX
LIST OF ACRONYMS XI
LIST OF SYMBOLS XIII
1 INTRODUCTION 1
1.1 MOTIVATION 1
1.2 STRUCTURE OF THIS THESIS 5
1.3 SYSTEM SETUP 7
2 MATHEMATICAL PRELIMINARIES 9
2.1 MATRIX THEORETIC PRELIMINARIES 9
2.1.1 GENERAL MATRIX PENCILS 9
2.1.2 EVEN MATRIX PENCILS AND THEIR CONDENSED FORMS 14
2.1.3 SKEW-HATNILTONIAN/HAMILTONIAN MATRIX PENCILS 19
2.2 SYSTEM THEORETIC BASICS 22
2.2.1 DESCRIPTOR SYSTEMS, BEHAVIORS, AND STABILITY 22
2.2.2 CONTROLLABILITY, STABILIZABILITY, OBSERVABILITY, AND DETECTABILITY
24
2.2.3 FREQUENCY DOMAIN ANALYSIS 28
LAPLACE TRANSFORMATION AND TRANSFER FUNCTIONS 28
POLYNOMIAL AND RATIONAL MATRICES 30
SOME RATIONAL FUNCTION SPACES 33
2.2.4 ZERO DYNAMICS AND OUTER SYSTEMS 34
3 LINEAR-QUADRATIC CONTROL THEORY FOR DIFFERENTIAL-ALGEBRAIC EQUATIONS
38
3.1 INTRODUCTION 38
3.2 STATE AND FEEDBACK TRANSFORMATIONS 45
3.3 KALMAN-YAKUBOVICH-POPOV LEMMA 48
3.4 EVEN MATRIX PENCILS AND DESCRIPTOR LUR'E EQUATIONS 53
3.5 STABILIZING, ANTI-STABILIZING, AND EXTREMAL SOLUTIONS 70
HTTP://D-NB.INFO/1076282202
CONTENTS
3.6 SPECTRAL FACTORIZATION 72
3.7 NONPOSITIVE SOLUTIONS 74
3.8 LINEAR-QUADRATIC OPTIMAL CONTROL 84
3.8.1 OPTIMAL CONTROL WITH ZERO TERMINAL CONDITION 84
3.8.2 OPTIMAL CONTROL WITH FREE TERMINAL CONDITION 10G
3.9 DISSIPATIVE AND CYCLO-DISSIPATIVE SYSTEMS L09
3.9.1 SYSTEMS WITH GENERAL QUADRATIC SUPPLY RATES 109
3.9.2 CONTRACTIVE AND PASSIVE SYSTEMS 120
3.10 NORMALIZED COPRIME FACTORIZATIONS 124
3 11 INNER-OUTER FACTORIZATIONS 134
3.12 SUMMARY AND OUTLOOK 141
4 SYSTEMS WITH COUNTERCLOCKWISE INPUT/OUTPUT DYNAMICS 144
4.1 INTRODUCTION 144
4.2 SYSTEMS WITH COUNTERCLOCKWISE INPUT/OUTPUT DYNAMICS AND NEGATIVE
IMAGINARY TRANSFER FUNCTIONS 145
4.3 SPECTRAL CHARACTERIZATIONS FOR NEGATIVE IMAGINARINESS 148
4.4 ENFORCEMENT OF NEGATIVE IMAGINARINESS 152
4.4.1 SOME USEFUL RESULTS 152
4.4.2 CHOICE OF THE NEW FREQUENCIES 155
4.4.3 CHOICE OF THE SYSTEM NORM 156
4.4.4 ENFORCEMENT PROCEDURE 159
4.4.5 ENFORCING SYMMETRY OF THE POLYNOMIAL PART 161
4.4.6 THE OVERALL PROCESS 161
4.4.7 REFORMULATION OF THE ODD EIGENVALUE PROBLEM 162
4.4.8 COMPUTATION OF THE EIGENVECTORS 164
THE ALGORITHM 164
IMPLEMENTATION AND NUMERICAL EXPERIMENTS 168
4.4.9 AN ILLUSTRATIVE EXAMPLE 171
4.5 CONCLUSIONS AND OUTLOOK 173
5 COMPUTATION OF THE COMPLEX CYCLO-DISSIPATIVITY RADIUS 175
5.1 INTRODUCTION 175
5.2 THE CYCLO-DISSIPATIVITY RADIUS 177
5.3 PERTURBATIONS OF THE SINGULAR PART AND THE DEFECTIVE INFINITE
EIGENVALUES 180
5.3.1 PERTURBATION OF THE SINGULAR PART 180
5.3.2 PERTURBATION OF THE DEFECTIVE INFINITE EIGENVALUES 186
5.4 COMPUTATION OF THE COMPLEX CYCLO-DISSIPATIVITY RADIUS 193
5.5 NUMERICAL RESULTS 199
5.5.1 ILLUSTRATIVE EXAMPLES 199
5.5.2 LIMITATIONS OF THE METHOD 202
CONTENTS
5.6 SUMMARY AND OPEN PROBLEMS 204
6 COMPUTATION OF THE WCO-NORM FOR LARGE-SCALE DESCRIPTOR SYSTEMS 205
6.1 INTRODUCTION 205
6 2 THE PSEUDOPOLC SET APPROACH 208
6.2.1 COMPLEX WOO-RADIUS AND HOO-NORM 208
6.2.2 COMPUTATION OF THE E-PSEUDOPOLC SET ABSCISSA 214
DERIVATION OF THE BASIC ALGORITHM 214
CHOICE OF THE EIGENVALUES 218
ALGORITHMIC DETAILS 220
FIXED POINT ANALYSIS 221
LOCAL CONVCIGCNCC AND ERROR ANALYSIS 224
6.2.3 NEWTON'S METHOD FOR COMPUTING THE COMPLEX W
00
-R,ADIUS . . 225
6.2.4 COMPARISON WITH THE METHOD OF GUGLIEHNI, GURBIIZBALABAN,
AND OVERTON 226
6.2.5 NUMERICAL RESULTS 229
TEST SETUP . 229
TEST RESULTS 229
COMPARISON OF DOMINANCE MEASURES 231
COMPARISON WITH OTHER METHODS 233
LIMITATIONS OF THE METHOD 235
6.3 THE EVEN PENCIL APPROACH 238
6.3 1 THCOICTICAL PRELIMINARIES AND ALGOL ITHM OUTLINE 238
6.3.2 STRUCTURED ITERATIVE EIGENSOLVERS 239
6.3.3 IMPLEMENTATION DETAILS 241
6.3.4 NUMERICAL RESULTS 243
TEST SETUP 243
TEST R.ESULTS AND COMPARISON WITH THE PSEUDOPOLC SET
APPROACH 243
6.4 CONCLUSIONS AND FUTURE RESEARCH PERSPECTIVES 245
7 SUMMARY AND OUTLOOK 248
BIBLIOGRAPHY 251
INDEX 269
THESES 275
STATEMENT OF SCIENTIFIC COOPERATIONS 279
DECLARATION OF HONOR/SCHRIFTLICHE EHRENERKLARUNG 283
III |
| any_adam_object | 1 |
| author | Voigt, Matthias 1986- |
| author_GND | (DE-588)142017590 |
| author_facet | Voigt, Matthias 1986- |
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| building | Verbundindex |
| bvnumber | BV043320929 |
| ctrlnum | (OCoLC)954280510 (DE-599)DNB1076282202 |
| dewey-full | 515.642 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.642 |
| dewey-search | 515.642 |
| dewey-sort | 3515.642 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-08-03T02:51:54Z |
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| isbn | 9783832541187 3832541187 |
| language | English |
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| physical | xviii, 284 Seiten Diagramme 21 cm |
| publishDate | 2015 |
| publishDateSearch | 2015 |
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| publisher | Logos Verlag Berlin GmbH |
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| spelling | Voigt, Matthias 1986- Verfasser (DE-588)142017590 aut On linear-quadratic optimal control and robustness of differential-algebraic systems von Dipl.-Math. Matthias Voigt Berlin Logos Verlag Berlin GmbH [2015] © 2015 xviii, 284 Seiten Diagramme 21 cm txt rdacontent n rdamedia nc rdacarrier Dissertation Otto-von-Guericke-Universität Magdeburg 2015 Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Otto-von-Guericke-Universität Magdeburg Systemtheorie Algebro-Differentialgleichungen Optimale und robuste Regelung Störungstheorie von Matrizen Numerische Methoden (DE-588)4113937-9 Hochschulschrift gnd-content Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s Optimale Kontrolle (DE-588)4121428-6 s DE-604 Logos Verlag Berlin (DE-588)1065538812 pbl B:DE-101 application/pdf http://d-nb.info/1076282202/04 Inhaltsverzeichnis X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=88f9d86631b8418f806a3291256391bb&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028741368&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Voigt, Matthias 1986- On linear-quadratic optimal control and robustness of differential-algebraic systems Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4229517-8 (DE-588)4121428-6 (DE-588)4113937-9 |
| title | On linear-quadratic optimal control and robustness of differential-algebraic systems |
| title_auth | On linear-quadratic optimal control and robustness of differential-algebraic systems |
| title_exact_search | On linear-quadratic optimal control and robustness of differential-algebraic systems |
| title_full | On linear-quadratic optimal control and robustness of differential-algebraic systems von Dipl.-Math. Matthias Voigt |
| title_fullStr | On linear-quadratic optimal control and robustness of differential-algebraic systems von Dipl.-Math. Matthias Voigt |
| title_full_unstemmed | On linear-quadratic optimal control and robustness of differential-algebraic systems von Dipl.-Math. Matthias Voigt |
| title_short | On linear-quadratic optimal control and robustness of differential-algebraic systems |
| title_sort | on linear quadratic optimal control and robustness of differential algebraic systems |
| topic | Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Differential-algebraisches Gleichungssystem Optimale Kontrolle Hochschulschrift |
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| work_keys_str_mv | AT voigtmatthias onlinearquadraticoptimalcontrolandrobustnessofdifferentialalgebraicsystems AT logosverlagberlin onlinearquadraticoptimalcontrolandrobustnessofdifferentialalgebraicsystems |
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