Introduction to the theory of differential inclusions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2002
|
| Series: | Graduate studies in mathematics
41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 226 S. |
| ISBN: | 9780821829776 0821829777 |
Staff View
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| 100 | 1 | |a Smirnov, Georgij V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to the theory of differential inclusions |c Georgi V. Smirnov |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2002 | |
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| 490 | 1 | |a Graduate studies in mathematics |v 41 | |
| 650 | 7 | |a GEOMETRIA DIFERENCIAL |2 larpcal | |
| 650 | 4 | |a Inclusions différentielles | |
| 650 | 4 | |a Differential inclusions | |
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Record in the Search Index
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| adam_text | Contents
Preface xi
Introduction xiij
Part 1. Foundations
Chapter 1. Convex Analysis 3
§1.1. Convex sets 3
§1.2. Convex functions 13
§1.3. Differential properties of convex functions 24
§1.4. Problems 30
Chapter 2. Set Valued Analysis 31
§2.1. Set valued maps 31
§2.2. Derivatives of set valued maps 37
§2.3. Lipschitzian approximations 41
§2.4. Extension theorem 44
§2.5. Fixed point theorems 47
§2.6. Convex processes 49
§2.7. Structure of a convex process 56
§2.8. Problems 61
vii
Chapter 3. Nonsmooth Analysis 65
§3.1. Method of metric approximations 65
§3.2. Mordukhovich normal cone 67
§3.3. Separation theorem for nonconvex sets 72
§3.4. Nonsmooth calculus 75
§3.5. Lagrange multipliers 82
§3.6. Problems 83
Part 2. Differential Inclusions
Chapter 4. Existence Theorems 87
§4.1. Background notes 88
§4.2. Lipschitzian differential inclusions 90
§4.3. Upper semi continuous differential inclusions 96
§4.4. Discontinuous differential equations 103
§4.5. Existence of optimal solutions 106
§4.6. Dependence on initial conditions 109
§4.7. Discrete approximations 113
§4.8. Problems 116
Chapter 5. Viability and Invariance 119
§5.1. Monotone solutions to a differential inclusion 119
§5.2. Viability problem 122
§5.3. Invariant sets 127
§5.4. Existence of periodic solutions 130
§5.5. Pursuit in a differential game 132
§5.6. Problems 135
Chapter 6. Controllability 139
§6.1. Duality relation 139
§6.2. Controllability of convex processes 145
§6.3. Controllability at first approximation 147
§6.4. Controllability of some mechanical systems 152
§6.5. Problems 153
Chapter 7. Optimality 157
§7.1. Optimal solutions to discrete time inclusions 157
§7.2. Optimal solutions to differential inclusions 160
§7.3. Time optimal problem 165
§7.4. Problems 168
Chapter 8. Stability 171
§8.1. Lyapunov direct method 171
§8.2. Linear selectionable differential inclusions 176
§8.3. Weak asymptotic stability of convex processes 185
§8.4. First approximation techniques 189
§8.5. Stability of a missile uniform motion 194
§8.6. Problems 196
Chapter 9. Stabilization 199
§9.1. Lyapunov functions for convex processes 200
§9.2. Stabilization problem 202
§9.3. Weak asymptotic stability and stabilizability 205
§9.4. Stabilizers for some mechanical systems 208
§9.5. Problems 210
Comments 213
Bibliography 219
Index 225
|
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| isbn | 9780821829776 0821829777 |
| language | English |
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| physical | XVI, 226 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | American Math. Soc. |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Smirnov, Georgij V. Verfasser aut Introduction to the theory of differential inclusions Georgi V. Smirnov Providence, RI American Math. Soc. 2002 XVI, 226 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 41 GEOMETRIA DIFERENCIAL larpcal Inclusions différentielles Differential inclusions Differentialinklusion (DE-588)4149777-6 gnd rswk-swf Differentialinklusion (DE-588)4149777-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2092-5 Graduate studies in mathematics 41 (DE-604)BV009739289 41 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009727522&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smirnov, Georgij V. Introduction to the theory of differential inclusions Graduate studies in mathematics GEOMETRIA DIFERENCIAL larpcal Inclusions différentielles Differential inclusions Differentialinklusion (DE-588)4149777-6 gnd |
| subject_GND | (DE-588)4149777-6 |
| title | Introduction to the theory of differential inclusions |
| title_auth | Introduction to the theory of differential inclusions |
| title_exact_search | Introduction to the theory of differential inclusions |
| title_full | Introduction to the theory of differential inclusions Georgi V. Smirnov |
| title_fullStr | Introduction to the theory of differential inclusions Georgi V. Smirnov |
| title_full_unstemmed | Introduction to the theory of differential inclusions Georgi V. Smirnov |
| title_short | Introduction to the theory of differential inclusions |
| title_sort | introduction to the theory of differential inclusions |
| topic | GEOMETRIA DIFERENCIAL larpcal Inclusions différentielles Differential inclusions Differentialinklusion (DE-588)4149777-6 gnd |
| topic_facet | GEOMETRIA DIFERENCIAL Inclusions différentielles Differential inclusions Differentialinklusion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009727522&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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