Asymptotic behavior of dynamical and control systems under perturbation and discretization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2002
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| Series: | Lecture notes in mathematics
1783 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 231 S. graph. Darst. |
| ISBN: | 3540433910 |
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| 245 | 1 | 0 | |a Asymptotic behavior of dynamical and control systems under perturbation and discretization |c Lars Grüne |
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Record in the Search Index
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| adam_text | Table of Contents
1 Introduction: Dynamics, Perturbation and Discretization . 1
1.1 Starting Point 2
1.2 Different Approaches 4
1.3 Basic Idea 6
1.4 Outline of the Results 7
1.5 Open Questions and Future Research 10
2 Setup and Preliminaries 13
2.1 Continuous Time Systems 13
2.2 Discrete Time Systems 19
2.3 Sets, Distances and Limits 22
3 Strongly Attracting Sets 27
3.1 Strong Attraction 27
3.2 Robustness Concepts 29
3.3 Geometric Characterizations 34
3.4 Relation between Robustness Concepts 38
3.5 Lyapunov Function Characterization 43
3.6 Stability of Robustness Concepts 52
3.7 Inflated Systems 56
3.8 Discrete and Continuous Time Systems 64
4 Weakly Attracting Sets 69
4.1 Weak Attraction 69
4.2 Robustness Concepts 75
4.3 Geometric Characterizations 78
VIII Table of Contents
4.4 Relation between Robustness Concepts 82
4.5 Lyapunov Function Characterization 87
4.6 Stability of Robustness Concepts 96
4.7 Inflated Systems 100
4.8 Discrete and Continuous Time Systems 107
5 Relation between Discretization and Perturbation 113
5.1 Time Discretization: Theoretical Framework 113
5.2 Time Discretization: Numerical Schemes 117
5.3 Space Discretization 129
6 Discretizations of Attracting Sets 137
6.1 Strongly Attracting Sets 137
6.2 Strong Attractors 142
6.3 Subdivision Algorithm 148
6.4 Weakly Attracting Sets 151
7 Domains of Attraction 157
7.1 Definitions and Basic Properties 157
7.2 Zubov s Method 159
7.3 Robustness for Domains of Attraction 169
7.4 Domains of Attraction under One Step Discretizations 173
7.5 Subdivision Algorithm 178
7.6 Numerical Approximation of Zubov s Method 185
7.7 Reachable Sets 189
Appendices
A Viscosity Solutions 195
A.I Definition 195
A.2 Optimality Principles 196
B Comparison Functions 201
B.I Definition 201
B.2 Approximation by Smooth Functions 203
Table of Contents IX
C Numerical Examples 207
C.I Subdivision Algorithm: Test Examples 207
C.2 Subdivision Algorithm: Further Examples 212
C.3 Zubov s Method 215
Notation 219
References 221
Index 229
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:59:29Z |
| institution | BVB |
| isbn | 3540433910 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009735261 |
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| physical | IX, 231 S. graph. Darst. |
| publishDate | 2002 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Grüne, Lars 1967- Verfasser (DE-588)133659097 aut Asymptotic behavior of dynamical and control systems under perturbation and discretization Lars Grüne Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2002 IX, 231 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1783 Attracteurs (Mathématiques) Dynamique différentiable Développements asymptotiques Perturbation (Mathématiques) Systeemtheorie gtt Asymptotic expansions Attractors (Mathematics) Differentiable dynamical systems Perturbation (Mathematics) Dynamisches System (DE-588)4013396-5 gnd rswk-swf Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd rswk-swf Diskretisierung (DE-588)4012469-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Diskretisierung (DE-588)4012469-1 s Asymptotisches Lösungsverhalten (DE-588)4134367-0 s DE-604 Lecture notes in mathematics 1783 (DE-604)BV000676446 1783 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009735261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grüne, Lars 1967- Asymptotic behavior of dynamical and control systems under perturbation and discretization Lecture notes in mathematics Attracteurs (Mathématiques) Dynamique différentiable Développements asymptotiques Perturbation (Mathématiques) Systeemtheorie gtt Asymptotic expansions Attractors (Mathematics) Differentiable dynamical systems Perturbation (Mathematics) Dynamisches System (DE-588)4013396-5 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Diskretisierung (DE-588)4012469-1 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4134367-0 (DE-588)4012469-1 |
| title | Asymptotic behavior of dynamical and control systems under perturbation and discretization |
| title_auth | Asymptotic behavior of dynamical and control systems under perturbation and discretization |
| title_exact_search | Asymptotic behavior of dynamical and control systems under perturbation and discretization |
| title_full | Asymptotic behavior of dynamical and control systems under perturbation and discretization Lars Grüne |
| title_fullStr | Asymptotic behavior of dynamical and control systems under perturbation and discretization Lars Grüne |
| title_full_unstemmed | Asymptotic behavior of dynamical and control systems under perturbation and discretization Lars Grüne |
| title_short | Asymptotic behavior of dynamical and control systems under perturbation and discretization |
| title_sort | asymptotic behavior of dynamical and control systems under perturbation and discretization |
| topic | Attracteurs (Mathématiques) Dynamique différentiable Développements asymptotiques Perturbation (Mathématiques) Systeemtheorie gtt Asymptotic expansions Attractors (Mathematics) Differentiable dynamical systems Perturbation (Mathematics) Dynamisches System (DE-588)4013396-5 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Diskretisierung (DE-588)4012469-1 gnd |
| topic_facet | Attracteurs (Mathématiques) Dynamique différentiable Développements asymptotiques Perturbation (Mathématiques) Systeemtheorie Asymptotic expansions Attractors (Mathematics) Differentiable dynamical systems Perturbation (Mathematics) Dynamisches System Asymptotisches Lösungsverhalten Diskretisierung |
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