Continuous-Time Markov Jump Linear Systems:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2013
|
| Series: | Probability and its Applications
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 286 S. graph. Darst. |
| ISBN: | 9783642340994 |
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Record in the Search Index
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IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 MARKOV JUMP LINEAR SYSTEMS 1
1.2 SOME APPLICATIONS OF MJLS 7
1.3 PREREQUISITES AND GENERAL REMARKS 11
1.4 OVERVIEW O F THE CHAPTERS 11
1.5 HISTORICAL REMARKS 13
2 A FEW TOOLS AND NOTATIONS 15
2.1 OUTLINE O F THE CHAPTER 15
2.2 SOME BASIC NOTATION AND DEFINITIONS 15
2.3 SEMIGROUP OPERATORS AND INFINITESIMAL GENERATOR 16
2.4 THE FUNDAMENTAL THEOREM FOR DIFFERENTIAL EQUATIONS 17
2.5 CONTINUOUS-TIME MARKOV CHAINS 19
2.6 THE SPACE OF SEQUENCES O F N MATRICES 23
2.7 AUXILIARY RESULTS 2 6
2.8 LINEAR MATRIX INEQUALITIES 29
3 MEAN-SQUARE STABILITY 33
3.1 OUTLINE O F THE CHAPTER 33
3.2 THE MODELS AND PROBLEM STATEMENT 33
3.3 MAIN OPERATORS AND AUXILIARY RESULTS 36
3.4 MEAN-SQUARE STABILITY FOR THE HOMOGENEOUS CASE 44
3.4.1 MSS,~STS, AND THE SPECTRUM OF AN AUGMENTED MATRIX . . . 44 3.4.2
COUPLED LYAPUNOV EQUATIONS 47
3.4.3 SUMMARY 52
3.5 THE P ) AND JUMP DIFFUSION CASES 52
3.5.1 THE L R 2 (2, T , P ) DISTURBANCE CASE 53
3.5.2 THE JUMP DIFFUSION CASE 55
3.5.3 SUMMARY 58
3.6 MEAN-SQUARE STABILIZABILITY AND DETECTABILITY 59
3.6.1 DEFINITIONS AND LMIS CONDITIONS 59
IX
HTTP://D-NB.INFO/1025944577
IMAGE 2
X C O N T E N T S
3.6.2 MEAN-SQUARE STABILIZABILITY WITH 9 ( T ) PARTIALLY KNOWN . . 61
3.6.3 DYNAMIC OUTPUT MEAN-SQUARE STABILIZABILITY 64
3.7 HISTORICAL REMARKS 68
4 QUADRATIC OPTIMAL CONTROL WITH COMPLETE OBSERVATIONS 71
4.1 OUTLINE O F THE CHAPTER 71
4.2 NOTATION AND PROBLEM FORMULATION 71
4.3 DYNKIN'S FORMULA 74
4.4 THE FINITE-HORIZON OPTIMAL CONTROL PROBLEM 76
4.5 THE INFINITE-HORIZON OPTIMAL CONTROL PROBLEM 79
4.6 HISTORICAL REMARKS 81
5 H I OPTIMAL CONTROL WITH COMPLETE OBSERVATIONS 83
5.1 OUTLINE O F THE CHAPTER 83
5.2 ROBUST AND QUADRATIC MEAN-SQUARE STABILIZABILITY 83
5.3 CONTROLLABILITY, OBSERVABILITY GRAMIANS, AND THE //2 -NORM 85
5.4 H I CONTROL VIA CONVEX ANALYSIS 88
5.4.1 PRELIMINARIES 88
5.4.2 N EXACTLY KNOWN 89
5.4.3 N NOT EXACTLY KNOWN 91
5.5 THE CONVEX APPROACH AND THE CARE 92
5.6 HISTORICAL REMARKS 96
6 QUADRATIC AND H J OPTIMAL CONTROL WITH PARTIAL OBSERVATIONS . . . . 97
6.1 OUTLINE O F THE CHAPTER 97
6.2 FINITE-HORIZON QUADRATIC OPTIMAL CONTROL WITH PARTIAL OBSERVATIONS
98 6.2.1 PROBLEM STATEMENT 98
6.2.2 FILTERING PROBLEM 99
6.2.3 A SEPARATION PRINCIPLE FOR MJLS 105
6.3 THE HI CONTROL PROBLEM WITH PARTIAL OBSERVATIONS 112
6.3.1 PROBLEM STATEMENT 112
6.3.2 FILTERING H I PROBLEM 115
6.3.3 THE SEPARATION PRINCIPLE 119
6.3.4 AN LMIS APPROACH FOR THE H2 CONTROL PROBLEM 123
6.4 HISTORICAL REMARKS 126
7 BEST LINEAR FILTER WITH UNKNOWN (X(0 ? 0 ( 0 ) '27
7.1 OUTLINE OF THE CHAPTER 127
7.2 PRELIMINARIES 127
7.3 PROBLEM FORMULATION FOR THE FINITE-HORIZON CASE 129
7.4 MAIN RESULT FOR THE FINITE-HORIZON CASE 131
7.5 STATIONARY SOLUTION FOR THE ALGEBRAIC RICCATI EQUATION 136
7.6 STATIONARY FILTER 139
7.6.1 AUXILIARY RESULTS AND PROBLEM FORMULATION 139
7.6.2 SOLUTION FOR THE STATIONARY FILTERING PROBLEM VIA THE ARE . 147
7.7 HISTORICAL REMARKS 149
IMAGE 3
CONTENTS XI
8 HOO CONTROL 151
8.1 OUTLINE OF THE CHAPTER 151
8.2 DESCRIPTION O F THE PROBLEM 151
8.3 THE BOUNDED REAL LEMMA 153
8.3.1 PROBLEM FORMULATION AND MAIN RESULT 153
8.3.2 PROOF OF PROPOSITION 8.3 AND LEMMA 8.4 156
8.4 THE HOC CONTROL PROBLEM 165
8.5 STATIC STATE FEEDBACK 166
8.6 DYNAMIC OUTPUT FEEDBACK 167
8.6.1 MAIN RESULTS 168
8.6.2 ANALYSIS OF DYNAMIC CONTROLLERS 170
8.6.3 SYNTHESIS O F DYNAMIC CONTROLLERS 176
8.6.4 H Q O ANALYSIS AND SYNTHESIS ALGORITHMS 179
8.7 HISTORICAL REMARKS 181
9 DESIGN TECHNIQUES 1 83
9.1 OUTLINE O F THE CHAPTER 183
9.2 STABILITY RADIUS 183
9.3 A ROBUSTNESS MARGIN FOR 77 189
9.4 ROBUST CONTROL 193
9.4.1 PRELIMINARY RESULTS 194
9.4.2 ROBUST H I CONTROL 196
9.4.3 THE EQUALIZED CASE 199
9.4.4 ROBUST MIXED H J / //OO CONTROL 200
9.5 ROBUST LINEAR FILTERING PROBLEM VIA AN LMIS FORMULATION 201
9.5.1 THE LMIS FORMULATION 202
9.5.2 ROBUST FILTER 206
9.5.3 ARE APPROXIMATIONS FOR THE LMIS PROBLEM 208
9.6 HISTORICAL REMARKS 210
10 SOME NUMERICAL EXAMPLES 213
10.1 OUTLINE O F THE CHAPTER 213
10.2 AN EXAMPLE ON ECONOMICS 213
10.3 COUPLED ELECTRICAL MACHINES 217
10.3.1 PROBLEM STATEMENT 218
10.3.2 MEAN-SQUARE STABILIZATION 220
10.3.3 H 2 CONTROL 220
10.3.4 STABILITY RADIUS ANALYSIS 221
10.3.5 SYNTHESIS OF ROBUST CONTROLLERS 223
10.4 ROBUST CONTROL O F AN UNDERACTUATED ROBOTIC ARM 223
10.5 AN EXAMPLE O F A STATIONARY FILTER 226
10.6 HISTORICAL REMARKS 230
APPENDIX A COUPLED DIFFERENTIAL AND ALGEBRAIC RICCATI EQUATIONS . . .
231 A.L OUTLINE O F THE APPENDIX 231
A.2 COUPLED DIFFERENTIAL RICCATI EQUATIONS 231
A.3 MAXIMAL SOLUTION 237
IMAGE 4
XII C O N T E N T S
A.4 STABILIZING SOLUTION 244
A.5 FILTERING COUPLED ALGEBRAIC RICCATI EQUATIONS 246
A.6 ASYMPTOTIC CONVERGENCE 248
A.7 FILTERING DIFFERENTIAL AND ALGEBRAIC RICCATI EQUATION FOR UNKNOWN 0
( 0 252
APPENDIX B THE ADJOINT OPERATOR AND SOME AUXILIARY RESULTS 257 B.L
OUTLINE O F THE APPENDIX 257
B.2 PRELIMINARIES 257
B.3 MAIN RESULTS 258
NOTATION AND CONVENTIONS 263
REFERENCES 27 1
INDEX 285 |
| any_adam_object | 1 |
| author | Costa, Oswaldo Luiz do Valle Fragoso, Marcelo Dutra Todorov, Marcos G. |
| author_facet | Costa, Oswaldo Luiz do Valle Fragoso, Marcelo Dutra Todorov, Marcos G. |
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| author_sort | Costa, Oswaldo Luiz do Valle |
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| dewey-ones | 519 - Probabilities and applied mathematics 003 - Systems |
| dewey-raw | 519.23 003.76 |
| dewey-search | 519.23 003.76 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| spelling | Costa, Oswaldo Luiz do Valle Verfasser aut Continuous-Time Markov Jump Linear Systems Oswaldo L. V. Costa ; Marcelo D. Fragoso ; Marcos G. Todorov Berlin ; Heidelberg Springer 2013 XII, 286 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probability and its Applications Markov-Sprungprozess (DE-588)4427907-3 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 gnd rswk-swf Lineares System (DE-588)4125617-7 gnd rswk-swf Markov-Sprungprozess (DE-588)4427907-3 s Lineares System (DE-588)4125617-7 s Stochastische Kontrolltheorie (DE-588)4263657-7 s DE-604 Fragoso, Marcelo Dutra Verfasser aut Todorov, Marcos G. Verfasser aut X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4121732&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025497656&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Costa, Oswaldo Luiz do Valle Fragoso, Marcelo Dutra Todorov, Marcos G. Continuous-Time Markov Jump Linear Systems Markov-Sprungprozess (DE-588)4427907-3 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Lineares System (DE-588)4125617-7 gnd |
| subject_GND | (DE-588)4427907-3 (DE-588)4263657-7 (DE-588)4125617-7 |
| title | Continuous-Time Markov Jump Linear Systems |
| title_auth | Continuous-Time Markov Jump Linear Systems |
| title_exact_search | Continuous-Time Markov Jump Linear Systems |
| title_full | Continuous-Time Markov Jump Linear Systems Oswaldo L. V. Costa ; Marcelo D. Fragoso ; Marcos G. Todorov |
| title_fullStr | Continuous-Time Markov Jump Linear Systems Oswaldo L. V. Costa ; Marcelo D. Fragoso ; Marcos G. Todorov |
| title_full_unstemmed | Continuous-Time Markov Jump Linear Systems Oswaldo L. V. Costa ; Marcelo D. Fragoso ; Marcos G. Todorov |
| title_short | Continuous-Time Markov Jump Linear Systems |
| title_sort | continuous time markov jump linear systems |
| topic | Markov-Sprungprozess (DE-588)4427907-3 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Lineares System (DE-588)4125617-7 gnd |
| topic_facet | Markov-Sprungprozess Stochastische Kontrolltheorie Lineares System |
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