Stochastic H 2/H[infinity symbol] control a Nash game approach
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CRC Press, Taylor & Francis Group
[2017]
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| 100 | 1 | |a Zhang, Weihai |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic H 2/H[infinity symbol] control |b a Nash game approach |c Weihai Zhang, Lihua Xie, Bor-Sen Chen |
| 264 | 1 | |a Boca Raton |b CRC Press, Taylor & Francis Group |c [2017] | |
| 264 | 4 | |c © 2017 | |
| 300 | |a xix, 369 pages |b illustrations (black and white) |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Game theory / fast / (OCoLC)fst00937501 | |
| 650 | 4 | |a Stochastic control theory / fast / (OCoLC)fst01133503 | |
| 650 | 4 | |a Technology / ukslc | |
| 650 | 4 | |a Stochastic control theory | |
| 650 | 4 | |a Game theory | |
| 650 | 4 | |a Game theory | |
| 650 | 4 | |a Stochastic control theory | |
| 650 | 4 | |a Technology | |
| 650 | 0 | 7 | |a Stochastische Kontrolltheorie |0 (DE-588)4263657-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Xie, Lihua |e Verfasser |4 aut | |
| 700 | 1 | |a Chen, Bor-Sen |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804178532486610944 |
|---|---|
| adam_text | Contents
Preface *x
List of Tables xiii
List of Figures xv
Symbols and Acronyms xvii
1 Mathematical Preliminaries 1
1.1 Stochastic Differential Equations................................. 1
1.1.1 Existence and uniqueness of solutions..................... 1
1.1.2 Ito’s formula............................................. 6
1.1.3 Various definitions of stability......................... 10
1.2 Generalized Lyapunov Operators................................... 12
1.3 Basic Concepts of Stochastic Systems ............................ 17
1.3.1 Exact observability...................................... 17
1.3.2 Exact detectability...................................... 23
1.3.3 Mean square stabilization................................ 26
1.4 Notes and References............................................. 28
2 Linear Continuous-Time Stochastic H2J H00 Control 29
2.1 Introduction..................................................... 29
2.2 Finite Horizon H2/Hac Control ................................... 30
2.2.1 Definitions and lemmas................................... 31
2.2.2 Finite horizon stochastic bounded real lemma (SBRL) . . 34
2.2.3 Finite horizon stochastic LQ control..................... 39
2.2.4 Conditions for the existence of Nash equilibrium strategies 41
2.2.5 Main results............................................. 44
2.2.6 Unified treatment of H2, Hoo and mixed H2/H yo control
problems................................................. 52
2.3 Infinite Horizon H2jControl...................................... 55
2.3.1 Two Lyapunov-type theorems............................... 57
2.3.2 Infinite horizon stochastic LQ control................... 61
2.3.3 Infinite horizon SBRL.................................... 70
2.3.4 Stochastic H2/H00 control................................ 76
2.4 Relationship between Stochastic H2/Hao and Nash Game .... 84
2.5 Algorithm for Solving Coupled GAREs ............................. 87
v
Vi
Contents
2.6 Notes and References................................................. 88
3 Linear Discrete-Time Stochastic H2/Control 91
3.1 Finite Horizon H2/Hoo Control ....................................... 91
3.1.1 Definitions........................................... 92
3.1.2 Two identities........................................ 94
3.1.3 Finite horizon SBRL................................... 96
3.1.4 Discrete-time stochastic LQ control................... 99
3.1.5 Finite horizon 7/2/7/00 with (x, ^-dependent noise . . . 100
3.1.6 Unified treatment of H2, // 0 and H2/H00 control .... 103
3.1.7 A numerical example.................................. 106
3.1.8 H2/Hog control of systems with (x. u)~ and (x. ?/, ?;)-dependent
noise ...................................................... 107
3.2 Two-Person Non-Zero Sum Nash Game .................................. 109
3.3 Infinite Horizon i72/7/oo Control................................... Ill
3.3.1 Preliminaries........................................ 112
3.3.2 Standard LQ control result........................... 117
3.3.3 An SBRL.............................................. 120
3.3.4 7/2/7/00 control with (.r. t )-dependent noise 125
3.3.5 Numerical algorithms................................. 133
3.3.6 T/s/T/oo control with (x, u)- and (x. u. i )~dependent noise 139
3.4 Infinite Horizon Indefinite LQ Control ............................. 141
3.5 Comments on Stochastic H2/Hr^ and Nash Game....................... 147
3.6 Notes and References 147
4 7/2/7/00 Control for Linear Discrete Time-Varying Stochastic Systems 149
4.1 Stability and Uniform Detectability................................. 149
4.2 Lyapunov-Type Theorem under Uniform Detectability................... 156
4.3 Exact Detectability ................................................ 161
4.4 Lyapunov-Type Theorems for Periodic Systems under Exact De-
tectability ........................................................... 166
4.5 Further Remarks on LDTV Systems .................................. 168
4.6 Infinite Horizon Time-Varying T/2/7/oo Control...................... 169
4.7 Notes and References................................................ 172
5 Linear Markovian Jump Systems with Multiplicative Noise 173
5.1 Introduction........................................................ 173
5.2 Finite Horizon 7/2/7/00 Control of Discrete-Time Markov Jump
Systems ............................................................ 174
5.2.1 An SBRL..................................................... 175
5.2.2 Results on the 7/2/7/00 control ............................ 179
5.2.3 Algorithm and numerical example............................. 181
5.2.4 Unified treatment of 772, 7/oo and 772/7/oc control based
on Nash game .............................................. 182
5.3 Infinite Horizon Discrete Time-Varying 7/2/7/00 Control ............ 187
Contents vii
5.3.1 Definitions and preliminaries........................... 188
5.3.2 AnSBRL.................................................. 189
5.3.3 Main result ............................................ 193
5.3.4 An economic example..................................... 196
5.4 Infinite Horizon Discrete Time-Invariant H2/Hoo Control........... 197
5.4.1 Stability, stabilization, and SBRL...................... 199
5.4.2 Exact detectability and extended Lyapunov theorem . . . . 201
5.4.3 Main result and numerical algorithm.....................203
5.5 Finite Horizon //2///00 Control of Continuous-Time Systems . . 207
5.5.1 Definitions and lemmas.....................................208
5.5.2 Nash equilibrium strategy and H2/Hog control............211
5.6 Infinite Horizon Continuous-Time//2/iToo Control...................215
5.6.1 A moment equation..........................................215
5.6.2 Exact observability and detectability .....................217
5.6.3 Comments on the 7/2/7/00 control...........................220
5.7 Notes and References............................................ . 221
6 Nonlinear Continuous-Time Stochastic and 7/2/7/00 Controls 223
6.1 Dissipative Stochastic Systems ................................... 223
6.2 Observability and Detectability....................................227
6.3 Infinite Horizon H^ Control . . 229
6.4 Finite Horizon Nonlinear Ha0 Control ..............................236
6.5 T/qo Control of More General Stochastic Nonlinear Systems . 241
6.6 Finite Horizon 7/2/7/00 Control ...................................250
6.7 Notes and References ............................................. 257
7 Nonlinear Stochastic Hoo and //2///oo Filtering 259
7.1 Nonlinear Hqq Filtering: Delay-Free Case...........................259
7.1.1 Lemmas and definitions ....................................260
7.1.2 Main results...............................................261
7.2 Suboptimal Mixed 7/2/7/00 Filtering................................266
7.3 LMI-Based Approach for Quasi-Linear Filter Design .... 268
7.4 Suboptimal Mixed 7/2/7/00 Filtering of Quasi-Linear Systems . . 274
7.5 Numerical Example..................................................277
7.6 Nonlinear Filtering: Time-Delay Case............................278
7.6.1 Definitions and lemmas.....................................278
7.6.2 Main results...............................................285
7.7 Luenberger-Type Linear Time-Delay Hoo Filtering ...................288
7.8 Notes and References ..............................................291
8 Some Further Research Topics in Stochastic 7/2/T/oo Control 293
8.1 Stochastic 7/2/7/00 Control with Random Coefficients ..............293
8.1.1 SBRL and stochastic LQ lemma.............................294
8.1.2 Mixed 7/2/7/00 control................................... 296
8.1.3 //oo control.......................................... 298
Contents
viii
8.1.4 Some unsolved problems .................................301
8.2 Nonlinear Discrete-Time Stochastic H2/Hoo Control ...............302
8.2.1 Dissipation, ¿2-gain and SBRL................................303
8.2.2 Observability and detectability .............................306
8.2.3 Review of martingale theory..................................307
8.2.4 LaSalle-type theorems........................................308
8.2.5 Difficulties in affine nonlinear discrete H2/H00 control . . 316
8.3 Singular Stochastic H2/Hc 0 Control..................................316
8.3.1 Lemma and definition ........................................317
8.3.2 Asymptotical mean square admissibility.......................318
8.3.3 An illustrative example......................................324
8.3.4 Problems in H2/i7oo control..................................325
8.4 Mean-Field Stochastic H2/if00 Control ................................326
8.4.1 Definition for H2/i7oo control...............................326
8.4.2 Finite horizon SBRL..........................................327
8.4.3 Mean-field stochastic LQ control.............................336
8.4.4 H2/Hoo control with (x, t;)-dependent noise..................337
8.4.5 Further research problems....................................341
8.5 Notes and References..................................................341
References 343
Index
361
Electrical Systems and Controls
Stochastic HJH Control
2. oo
Stochastic Control: A Nash Game Approach presents the
latest results in stochastic H2 = H1 control and filtering based on the Nash
game approach. After providing some basics of stochastic differential
equations, stochastic stability, stochastic observability and detectability,
the book solves the H2 = /-/, control for linear ltd systems and establish-
es a relationship between the H2=H1 control and two-person non-zero
sum Nash game. It then discusses the control for linear discrete
time-invariant systems with multiplicative noise, then focuses on linear
discrete time-varying systems. After a discussion of mixed control
for linear Markov jump systems with multiplicative noise, it establishes
the equivalence between stochastic dissipativity and the solvability of
nonlinear Lure.
The next chapter can be viewed as an extension of deterministic non-
linear control. The penultimate chapter is concerned with nonlinear
H_ and H2- H, filters of ltd systems, which have potential applications in
communication and signal processing. Finally, the authors present some
further research topics in stochastic control, including the
control of the following systems: (i) stochastic ltd systems with random
coefficients; (ii) nonlinear discrete-time stochastic systems with multipli-
cative noise; (iii) singular stochastic ltd systems and singular discrete-time
systems with multiplicative noise; and (iv) mean-field stochastic systems.
At the end of each chapter there is a brief review of related background
knowledge and further research topics.
Klbbbl
ISBN: =|70-l-MbbS-73b4-B
III
014fc b S73L42
TO
□ 0
www.crcpress.com
|
| any_adam_object | 1 |
| author | Zhang, Weihai Xie, Lihua Chen, Bor-Sen |
| author_facet | Zhang, Weihai Xie, Lihua Chen, Bor-Sen |
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| author_sort | Zhang, Weihai |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)1057700923 (DE-599)BVBBV044945350 |
| dewey-full | 629.8/312 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.8/312 |
| dewey-search | 629.8/312 |
| dewey-sort | 3629.8 3312 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| id | DE-604.BV044945350 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:05:28Z |
| institution | BVB |
| isbn | 9781466573642 1466573643 |
| language | English |
| lccn | 017285426 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030338189 |
| oclc_num | 1057700923 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | xix, 369 pages illustrations (black and white) 24 cm |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | CRC Press, Taylor & Francis Group |
| record_format | marc |
| spelling | Zhang, Weihai Verfasser aut Stochastic H 2/H[infinity symbol] control a Nash game approach Weihai Zhang, Lihua Xie, Bor-Sen Chen Boca Raton CRC Press, Taylor & Francis Group [2017] © 2017 xix, 369 pages illustrations (black and white) 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Game theory / fast / (OCoLC)fst00937501 Stochastic control theory / fast / (OCoLC)fst01133503 Technology / ukslc Stochastic control theory Game theory Technology Stochastische Kontrolltheorie (DE-588)4263657-7 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 s DE-604 Xie, Lihua Verfasser aut Chen, Bor-Sen Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030338189&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030338189&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Zhang, Weihai Xie, Lihua Chen, Bor-Sen Stochastic H 2/H[infinity symbol] control a Nash game approach Game theory / fast / (OCoLC)fst00937501 Stochastic control theory / fast / (OCoLC)fst01133503 Technology / ukslc Stochastic control theory Game theory Technology Stochastische Kontrolltheorie (DE-588)4263657-7 gnd |
| subject_GND | (DE-588)4263657-7 |
| title | Stochastic H 2/H[infinity symbol] control a Nash game approach |
| title_auth | Stochastic H 2/H[infinity symbol] control a Nash game approach |
| title_exact_search | Stochastic H 2/H[infinity symbol] control a Nash game approach |
| title_full | Stochastic H 2/H[infinity symbol] control a Nash game approach Weihai Zhang, Lihua Xie, Bor-Sen Chen |
| title_fullStr | Stochastic H 2/H[infinity symbol] control a Nash game approach Weihai Zhang, Lihua Xie, Bor-Sen Chen |
| title_full_unstemmed | Stochastic H 2/H[infinity symbol] control a Nash game approach Weihai Zhang, Lihua Xie, Bor-Sen Chen |
| title_short | Stochastic H 2/H[infinity symbol] control |
| title_sort | stochastic h 2 h infinity symbol control a nash game approach |
| title_sub | a Nash game approach |
| topic | Game theory / fast / (OCoLC)fst00937501 Stochastic control theory / fast / (OCoLC)fst01133503 Technology / ukslc Stochastic control theory Game theory Technology Stochastische Kontrolltheorie (DE-588)4263657-7 gnd |
| topic_facet | Game theory / fast / (OCoLC)fst00937501 Stochastic control theory / fast / (OCoLC)fst01133503 Technology / ukslc Stochastic control theory Game theory Technology Stochastische Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030338189&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030338189&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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