Analysis, controllability and optimization of time discrete systems and dynamical games:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo
Springer
2003
|
| Series: | Lecture notes in economics and mathematical systems
529 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 186 S. 24 cm |
| ISBN: | 3540403272 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
1 Uncontrolled Systems 1
1.1 The Autonomous Case 1
1.1.1 Definitions and Elementary Properties 1
1.1.2 Localization of Limit Sets with the Aid of
Lyapunov Functions 6
1.1.3 Stability Based on Lyapunov s Method 8
1.1.4 Stability of Fixed Points via Linearisation 13
1.1.5 Linear Systems 16
1.1.6 Applications 21
1.2 The Non-Autonomous Case 32
1.2.1 Definitions and Elementary Properties 32
1.2.2 Stability Based on Lyapunov s Method 35
1.2.3 Linear Systems 38
1.2.4 Application to a Model for the Process of Hemo-Dialysis 43
2 Controlled Systems 47
2.1 The Autonomous Case 47
2.1.1 The Problem of Fixed Point Controllability 47
2.1.2 Null-Controllability of Linear Systems 57
2.1.3 A Method for Solving the Problem of Null-Controllability 65
2.1.4 Stabilization of Controlled Systems 70
2.1.5 Applications 73
2.2 The Non-Autonomous Case 80
2.2.1 The Problem of Fixed Point Controllability 80
2.2.2 The General Problem of Controllability 83
2.2.3 Stabilization of Controlled Systems 86
2.2.4 The Problem of Reachability 89
3 Controllability and Optimization 93
3.1 The Control Problem 93
3.2 A Game Theoretical Solution 95
XII Contents
3.2.1 The Cooperative Case 95
3.2.2 The Non-Cooperative Case 99
3.2.3 The Linear Case 103
3.3 Local Controllability 106
3.4 An Emission Reduction Model 107
3.4.1 A Non-Cooperative Treatment 107
3.4.2 A Cooperative Treatment 116
3.4.3 Conditions for the Core to be Non-Empty 118
3.4.4 Further Conditions for the Core to be Non-Empty 122
3.4.5 A Second Cooperative Treatment 128
3.5 A Dynamical Method for Finding a Nash Equilibrium 136
3.5.1 The Goal-Cost-Game 136
3.5.2 Necessary Conditions for a Nash Equilibrium 137
3.5.3 The Method 139
3.6 Evolution Matrix Games 141
3.6.1 Definition of the Game and Evolutionary Stability 141
3.6.2 A Dynamical Method for Finding an Evolutionary
Stable State 147
3.7 A General Cooperative n-Person Goal-Cost-Game 151
3.7.1 The Game 151
3.7.2 A Cooperative Treatment 152
3.7.3 Necessary and Sufficient Conditions for a Stable
Grand Coalition 153
3.8 A Cooperative Treatment of an n-Person Cost-Game 155
3.8.1 The Game and a First Cooperative Treatment 155
3.8.2 Transformation of the Game into a
Cooperative Game 157
3.8.3 Sufficient Conditions for a Stable Grand Coalition 158
3.8.4 Further Cooperative Treatments 160
3.8.5 Pareto Optima as Cooperative Solutions of the Game .. 162
A Appendix 167
A.I The Core of a Cooperative n-Person Game 167
A.2 The Core of a Linear Production Game 173
A.3 Weak Pareto Optima: Necessary and Sufficient Conditions .... 177
A.4 Duality 179
B Bibliographical Remarks 181
References 183
Index 185
About the Authors 187
|
| adam_txt |
Contents
1 Uncontrolled Systems 1
1.1 The Autonomous Case 1
1.1.1 Definitions and Elementary Properties 1
1.1.2 Localization of Limit Sets with the Aid of
Lyapunov Functions 6
1.1.3 Stability Based on Lyapunov's Method 8
1.1.4 Stability of Fixed Points via Linearisation 13
1.1.5 Linear Systems 16
1.1.6 Applications 21
1.2 The Non-Autonomous Case 32
1.2.1 Definitions and Elementary Properties 32
1.2.2 Stability Based on Lyapunov's Method 35
1.2.3 Linear Systems 38
1.2.4 Application to a Model for the Process of Hemo-Dialysis 43
2 Controlled Systems 47
2.1 The Autonomous Case 47
2.1.1 The Problem of Fixed Point Controllability 47
2.1.2 Null-Controllability of Linear Systems 57
2.1.3 A Method for Solving the Problem of Null-Controllability 65
2.1.4 Stabilization of Controlled Systems 70
2.1.5 Applications 73
2.2 The Non-Autonomous Case 80
2.2.1 The Problem of Fixed Point Controllability 80
2.2.2 The General Problem of Controllability 83
2.2.3 Stabilization of Controlled Systems 86
2.2.4 The Problem of Reachability 89
3 Controllability and Optimization 93
3.1 The Control Problem 93
3.2 A Game Theoretical Solution 95
XII Contents
3.2.1 The Cooperative Case 95
3.2.2 The Non-Cooperative Case 99
3.2.3 The Linear Case 103
3.3 Local Controllability 106
3.4 An Emission Reduction Model 107
3.4.1 A Non-Cooperative Treatment 107
3.4.2 A Cooperative Treatment 116
3.4.3 Conditions for the Core to be Non-Empty 118
3.4.4 Further Conditions for the Core to be Non-Empty 122
3.4.5 A Second Cooperative Treatment 128
3.5 A Dynamical Method for Finding a Nash Equilibrium 136
3.5.1 The Goal-Cost-Game 136
3.5.2 Necessary Conditions for a Nash Equilibrium 137
3.5.3 The Method 139
3.6 Evolution Matrix Games 141
3.6.1 Definition of the Game and Evolutionary Stability 141
3.6.2 A Dynamical Method for Finding an Evolutionary
Stable State 147
3.7 A General Cooperative n-Person Goal-Cost-Game 151
3.7.1 The Game 151
3.7.2 A Cooperative Treatment 152
3.7.3 Necessary and Sufficient Conditions for a Stable
Grand Coalition 153
3.8 A Cooperative Treatment of an n-Person Cost-Game 155
3.8.1 The Game and a First Cooperative Treatment 155
3.8.2 Transformation of the Game into a
Cooperative Game 157
3.8.3 Sufficient Conditions for a Stable Grand Coalition 158
3.8.4 Further Cooperative Treatments 160
3.8.5 Pareto Optima as Cooperative Solutions of the Game . 162
A Appendix 167
A.I The Core of a Cooperative n-Person Game 167
A.2 The Core of a Linear Production Game 173
A.3 Weak Pareto Optima: Necessary and Sufficient Conditions . 177
A.4 Duality 179
B Bibliographical Remarks 181
References 183
Index 185
About the Authors 187 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Krabs, Werner 1934-2017 Pickl, Stefan 1967- |
| author_GND | (DE-588)120318741 (DE-588)12132799X |
| author_facet | Krabs, Werner 1934-2017 Pickl, Stefan 1967- |
| author_role | aut aut |
| author_sort | Krabs, Werner 1934-2017 |
| author_variant | w k wk s p sp |
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| callnumber-search | QA402.K68 2003 |
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| dewey-ones | 003 - Systems |
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| dewey-search | 003/.83 22 |
| dewey-sort | 13 283 222 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV023571170 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:39:43Z |
| indexdate | 2024-07-09T21:24:44Z |
| institution | BVB |
| isbn | 3540403272 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016886985 |
| oclc_num | 249657115 |
| open_access_boolean | |
| owner | DE-521 |
| owner_facet | DE-521 |
| physical | XII, 186 S. 24 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Krabs, Werner 1934-2017 Verfasser (DE-588)120318741 aut Analysis, controllability and optimization of time discrete systems and dynamical games Werner Krabs ; Stefan Wolfgang Pickl Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo Springer 2003 XII, 186 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 529 Discrete-time systems System analysis Control theory Differentiable dynamical systems Game theory Steuerbarkeit (DE-588)4134713-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches Spiel (DE-588)4121154-6 gnd rswk-swf Zeitdiskretes System (DE-588)4127297-3 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Zeitdiskretes System (DE-588)4127297-3 s Stabilität (DE-588)4056693-6 s Steuerbarkeit (DE-588)4134713-4 s DE-604 Dynamisches Spiel (DE-588)4121154-6 s Optimierung (DE-588)4043664-0 s Pickl, Stefan 1967- Verfasser (DE-588)12132799X aut Lecture notes in economics and mathematical systems 529 (DE-604)BV000000036 529 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016886985&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krabs, Werner 1934-2017 Pickl, Stefan 1967- Analysis, controllability and optimization of time discrete systems and dynamical games Lecture notes in economics and mathematical systems Discrete-time systems System analysis Control theory Differentiable dynamical systems Game theory Steuerbarkeit (DE-588)4134713-4 gnd Dynamisches System (DE-588)4013396-5 gnd Dynamisches Spiel (DE-588)4121154-6 gnd Zeitdiskretes System (DE-588)4127297-3 gnd Optimierung (DE-588)4043664-0 gnd Stabilität (DE-588)4056693-6 gnd |
| subject_GND | (DE-588)4134713-4 (DE-588)4013396-5 (DE-588)4121154-6 (DE-588)4127297-3 (DE-588)4043664-0 (DE-588)4056693-6 |
| title | Analysis, controllability and optimization of time discrete systems and dynamical games |
| title_auth | Analysis, controllability and optimization of time discrete systems and dynamical games |
| title_exact_search | Analysis, controllability and optimization of time discrete systems and dynamical games |
| title_exact_search_txtP | Analysis, controllability and optimization of time discrete systems and dynamical games |
| title_full | Analysis, controllability and optimization of time discrete systems and dynamical games Werner Krabs ; Stefan Wolfgang Pickl |
| title_fullStr | Analysis, controllability and optimization of time discrete systems and dynamical games Werner Krabs ; Stefan Wolfgang Pickl |
| title_full_unstemmed | Analysis, controllability and optimization of time discrete systems and dynamical games Werner Krabs ; Stefan Wolfgang Pickl |
| title_short | Analysis, controllability and optimization of time discrete systems and dynamical games |
| title_sort | analysis controllability and optimization of time discrete systems and dynamical games |
| topic | Discrete-time systems System analysis Control theory Differentiable dynamical systems Game theory Steuerbarkeit (DE-588)4134713-4 gnd Dynamisches System (DE-588)4013396-5 gnd Dynamisches Spiel (DE-588)4121154-6 gnd Zeitdiskretes System (DE-588)4127297-3 gnd Optimierung (DE-588)4043664-0 gnd Stabilität (DE-588)4056693-6 gnd |
| topic_facet | Discrete-time systems System analysis Control theory Differentiable dynamical systems Game theory Steuerbarkeit Dynamisches System Dynamisches Spiel Zeitdiskretes System Optimierung Stabilität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016886985&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
| work_keys_str_mv | AT krabswerner analysiscontrollabilityandoptimizationoftimediscretesystemsanddynamicalgames AT picklstefan analysiscontrollabilityandoptimizationoftimediscretesystemsanddynamicalgames |