Quadratic functionals in variational analysis and control theory:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Deutsch |
| Veröffentlicht: |
Berlin
Akad.-Verl.
1995
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Mathematical topics
6 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006690445&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 293 S. |
| ISBN: | 3055016564 |
Internformat
MARC
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| 100 | 1 | |a Kratz, Werner |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quadratic functionals in variational analysis and control theory |c Werner Kratz |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1995 | |
| 300 | |a 293 S. | ||
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| 650 | 7 | |a Calcul des variations |2 ram | |
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| 650 | 7 | |a Systèmes hamiltoniens |2 ram | |
| 650 | 4 | |a Calculus of variations | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Hamiltonian systems | |
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Datensatz im Suchindex
| _version_ | 1819344800857456640 |
|---|---|
| adam_text | Contents
0 Introduction 10
1 Preliminaries on Hamiltonian Systems and Picone s Identity 18
1.1 Hamiltonian Systems: Preliminaries 18
1.2 Picone s Identity 23
1.3 Calculus of Variations and Picone s Identity 27
1.4 Notes and References 32
2 Quadratic Functionals and Eigenvalue Problems: First Results 34
2.1 Homogeneous Quadratic Functionals: Preliminaries 34
2.2 Eigenvalue Problems: Preliminaries 41
2.3 Inhomogeneous Quadratic Functionals 47
2.4 First Results 60
2.5 The Classical Optimal Linear Regulator 66
2.6 Notes and References 70
3 Matrix Analysis 71
3.1 Rank Results and Certain Matrix Inequalities 71
3.2 Auxiliary Results on Symmetric Matrix Valued Functions 81
3.3 Limit Results on Symmetric Matrix Valued Functions 86
3.4 Index Results on Monotone Matrix Valued Functions 102
3.5 Topics in Linear Control Theory 106
3.6 Notes and References 122
4 Hamiltonian Systems: Oscillation and Identities 124
4.1 Preliminaries on Focal Points 124
4.2 Oscillation 131
4.3 Identities 136
4.4 Notes and References 139
5 Riccati Matrix Differential Equations: Inequalities and Index Re¬
sults 140
5.1 Inequalities 140
5.2 Index Results 145
Contents 9
5.3 Notes and References 147
6 Riccati Matrix Differential Equations: Asymptotics 148
6.1 Limit Results on Solutions of Hamiltonian Systems 148
6.2 Asymptotics in the Time Variable 151
6.3 Asymptotics of Sturm Liouville Equations 157
6.4 Asymptotics in the Eigenvalue Parameter 163
6.5 Asymptotics and Positive Definiteness 178
6.6 Notes and References 183
7 Main Results 185
7.1 Oscillation: Local Results 185
7.2 Oscillation: Global Results 189
7.3 Sturmian Theory 193
7.4 Oscillation: Supplements 199
7.5 Comparison of Eigenvalues 202
7.6 Existence of Eigenvalues 207
7.7 Rayleigh s Principle 212
7.8 Notes and References 227
8 Applications 229
8.1 The Optimal Linear Regulator and Rayleigh s Principle 229
8.2 Calculus of Variations and the Jacobi Condition 233
8.3 Sturm Liouville Eigenvalue Problems: Second Order 241
8.4 Sturm Liouville Eigenvalue Problems: General 252
8.5 Necessity of Assumptions and Miscellaneous Results 269
8.6 Discrete Systems and Perspectives 273
8.7 Notes and References 277
Bibliography 278
Index 290
|
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| id | DE-604.BV010079716 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:47:36Z |
| institution | BVB |
| isbn | 3055016564 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006690445 |
| oclc_num | 32236176 |
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| physical | 293 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical topics |
| series2 | Mathematical topics |
| spellingShingle | Kratz, Werner Quadratic functionals in variational analysis and control theory Mathematical topics Calcul des variations ram Commande, théorie de la ram Systèmes hamiltoniens ram Calculus of variations Control theory Hamiltonian systems Quadratisches Funktional (DE-588)4376656-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4376656-0 (DE-588)4032317-1 (DE-588)4062355-5 |
| title | Quadratic functionals in variational analysis and control theory |
| title_auth | Quadratic functionals in variational analysis and control theory |
| title_exact_search | Quadratic functionals in variational analysis and control theory |
| title_full | Quadratic functionals in variational analysis and control theory Werner Kratz |
| title_fullStr | Quadratic functionals in variational analysis and control theory Werner Kratz |
| title_full_unstemmed | Quadratic functionals in variational analysis and control theory Werner Kratz |
| title_short | Quadratic functionals in variational analysis and control theory |
| title_sort | quadratic functionals in variational analysis and control theory |
| topic | Calcul des variations ram Commande, théorie de la ram Systèmes hamiltoniens ram Calculus of variations Control theory Hamiltonian systems Quadratisches Funktional (DE-588)4376656-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Calcul des variations Commande, théorie de la Systèmes hamiltoniens Calculus of variations Control theory Hamiltonian systems Quadratisches Funktional Kontrolltheorie Variationsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006690445&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008671507 |
| work_keys_str_mv | AT kratzwerner quadraticfunctionalsinvariationalanalysisandcontroltheory |