Holdings: Discrete time Markov jump linear systems

Discrete time Markov jump linear systems:

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Bibliographic Details
Main Authors:	Costa, O. L. (Author), Fragoso, M. D. (Author), Marques, R. P. (Author)
Format:	Book
Language:	English
Published:	London Springer 2005
Edition:	1. ed.
Series:	Probability and its applications
Subjects:	Stochastische Kontrolltheorie Sprungprozess Markov-Sprungprozess Diskreter Markov-Prozess
Online Access:	Inhaltsverzeichnis
Physical Description:	X, 280 S. graph. Darst.
ISBN:	9781846280825

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Record in the Search Index

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adam_text	CONTENTS 1 MARKOV JUMP LINEAR SYSTEMS ............................. 1 1.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 SOME EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 PROBLEMS CONSIDERED IN THIS BOOK . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 SOME MOTIVATING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 A FEW WORDS ON OUR APPROACH. . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 BACKGROUND MATERIAL ...................................... 15 2.1 SOME BASICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 AUXILIARY RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 PROBABILISTIC SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 LINEAR SYSTEM THEORY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4.1 STABILITY AND THE LYAPUNOV EQUATION . . . . . . . . . . . . . . . . 21 2.4.2 CONTROLLABILITY AND OBSERVABILITY . . . . . . . . . . . . . . . . . . . . 23 2.4.3 THE ALGEBRAIC RICCATI EQUATION AND THE LINEAR- QUADRATIC REGULATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 LINEAR MATRIX INEQUALITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3 ON STABILITY ............................................... 29 3.1 OUTLINE OF THE CHAPTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 MAIN OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3 MSS: THE HOMOGENEOUS CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.1 MAIN RESULT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.2 EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3.3 PROOF OF THEOREM 3.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.3.4 EASY TO CHECK CONDITIONS FOR MEAN SQUARE STABILITY . . . 45 3.4 MSS: THE NON-HOMOGENEOUS CASE . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4.1 MAIN RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4.2 WIDE SENSE STATIONARY INPUT SEQUENCE . . . . . . . . . . . . . . . 49 3.4.3 THE * 2 -DISTURBANCE CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 VIII CONTENTS 3.5 MEAN SQUARE STABILIZABILITY AND DETECTABILITY . . . . . . . . . . . . . . . 57 3.5.1 DEFINITIONS AND TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.5.2 STABILIZABILITY WITH MARKOV PARAMETER PARTIALLY KNOWN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.6 STABILITY WITH PROBABILITY ONE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.6.1 MAIN RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.6.2 AN APPLICATION OF ALMOST SURE CONVERGENCE RESULTS . . . 66 3.7 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4 OPTIMAL CONTROL ........................................... 71 4.1 OUTLINE OF THE CHAPTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 THE FINITE HORIZON QUADRATIC OPTIMAL CONTROL PROBLEM. . . . . . 72 4.2.1 PROBLEM STATEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.2.2 THE OPTIMAL CONTROL LAW . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3 INFINITE HORIZON QUADRATIC OPTIMAL CONTROL PROBLEMS . . . . . . . . 78 4.3.1 DEFINITION OF THE PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.3.2 THE MARKOV JUMP LINEAR QUADRATIC REGULATOR PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.3.3 THE LONG RUN AVERAGE COST . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4 THE H 2 -CONTROL PROBLEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.4.1 PRELIMINARIES AND THE H 2 -NORM . . . . . . . . . . . . . . . . . . . . . . 82 4.4.2 THE H 2 -NORM AND THE GRAMMIANS . . . . . . . . . . . . . . . . . . . 83 4.4.3 AN ALTERNATIVE DEFINITION FOR THE H 2 -CONTROL PROBLEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4.4 CONNECTION BETWEEN THE CARE AND THE H 2 -CONTROL PROBLEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.5 QUADRATIC CONTROL WITH STOCHASTIC * 2 -INPUT . . . . . . . . . . . . . . . . . 90 4.5.1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.5.2 AUXILIARY RESULT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.5.3 THE OPTIMAL CONTROL LAW . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.5.4 AN APPLICATION TO A FAILURE PRONE MANUFACTURING SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.6 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5 FILTERING ................................................... 101 5.1 OUTLINE OF THE CHAPTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.2 FINITE HORIZON FILTERING WITH * ( K ) KNOWN . . . . . . . . . . . . . . . . . . 102 5.3 INFINITE HORIZON FILTERING WITH * ( K ) KNOWN . . . . . . . . . . . . . . . . . 109 5.4 OPTIMAL LINEAR FILTER WITH * ( K ) UNKNOWN . . . . . . . . . . . . . . . . . . 113 5.4.1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4.2 OPTIMAL LINEAR FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.4.3 STATIONARY LINEAR FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.5 ROBUST LINEAR FILTER WITH * ( K ) UNKNOWN . . . . . . . . . . . . . . . . . . . 119 5.5.1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.5.2 PROBLEM FORMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 CONTENTS IX 5.5.3 LMI FORMULATION OF THE FILTERING PROBLEM . . . . . . . . . . . . 124 5.5.4 ROBUST FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.6 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 6 QUADRATIC OPTIMAL CONTROL WITH PARTIAL INFORMATION ...... 131 6.1 OUTLINE OF THE CHAPTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.2 FINITE HORIZON CASE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.2.1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.2.2 A SEPARATION PRINCIPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.3 INFINITE HORIZON CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6.3.1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6.3.2 DEFINITION OF THE H 2 -CONTROL PROBLEM. . . . . . . . . . . . . . . . . 137 6.3.3 A SEPARATION PRINCIPLE FOR THE H 2 -CONTROL OF MJLS . . . . 139 6.4 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 7 H * -CONTROL ............................................... 143 7.1 OUTLINE OF THE CHAPTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 7.2 THE MJLS H * -LIKE CONTROL PROBLEM . . . . . . . . . . . . . . . . . . . . . . . 144 7.2.1 THE GENERAL PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.2.2 H * MAIN RESULT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 7.3 PROOF OF THEOREM 7.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7.3.1 SUFFICIENT CONDITION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7.3.2 NECESSARY CONDITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 7.4 RECURSIVE ALGORITHM FOR THE H * -CONTROL CARE . . . . . . . . . . . . . 162 7.5 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8 DESIGN TECHNIQUES AND EXAMPLES .......................... 167 8.1 SOME APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 8.1.1 OPTIMAL CONTROL FOR A SOLAR THERMAL RECEIVER . . . . . . . . 167 8.1.2 OPTIMAL POLICY FOR THE NATIONAL INCOME WITH A MULTIPLIERACCELERATOR MODEL . . . . . . . . . . . . . . . . . . . . . . . 169 8.1.3 ADDING NOISE TO THE SOLAR THERMAL RECEIVER PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 8.2 ROBUST CONTROL VIA LMI APPROXIMATIONS . . . . . . . . . . . . . . . . . . . 173 8.2.1 ROBUST H 2 -CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 8.2.2 ROBUST MIXED H 2 /H -CONTROL . . . . . . . . . . . . . . . . . . . . . . 182 8.2.3 ROBUST H * -CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 8.3 ACHIEVING OPTIMAL H * -CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 8.3.1 ALGORITHM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 8.3.2 H * -CONTROL FOR THE UARMII MANIPULATOR . . . . . . . . . . . . . . 189 8.4 EXAMPLES OF LINEAR FILTERING WITH * ( K ) UNKNOWN . . . . . . . . . . . . 197 8.4.1 STATIONARY LMMSE FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . 198 8.4.2 ROBUST LMMSE FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 8.5 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 X CONTENTS A COUPLED ALGEBRAIC RICCATI EQUATIONS ...................... 203 A.1 DUALITY BETWEEN THE CONTROL AND FILTERING CARE . . . . . . . . . . . 203 A.2 MAXIMAL SOLUTION FOR THE CARE . . . . . . . . . . . . . . . . . . . . . . . . . . 208 A.3 STABILIZING SOLUTION FOR THE CARE . . . . . . . . . . . . . . . . . . . . . . . . . 216 A.3.1 CONNECTION BETWEEN MAXIMAL AND STABILIZING SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 A.3.2 CONDITIONS FOR THE EXISTENCE OF A STABILIZING SOLUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 A.4 ASYMPTOTIC CONVERGENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 B AUXILIARY RESULTS FOR THE LINEAR FILTERING PROBLEM WITH * ( K ) UNKNOWN ............................................. 229 B.1 OPTIMAL LINEAR FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 B.1.1 PROOF OF THEOREM 5.9 AND LEMMA 5.11 . . . . . . . . . . . . . . . 229 B.1.2 STATIONARY FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 B.2 ROBUST FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 C AUXILIARY RESULTS FOR THE H 2 -CONTROL PROBLEM ............. 249 REFERENCES ..................................................... 257 NOTATION AND CONVENTIONS ..................................... 271 INDEX .......................................................... 277
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id	DE-604.BV023798099
illustrated	Illustrated
indexdate	2024-07-09T21:37:02Z
institution	BVB
isbn	9781846280825
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-017440301
oclc_num	249239776
open_access_boolean
owner	DE-634
owner_facet	DE-634
physical	X, 280 S. graph. Darst.
publishDate	2005
publishDateSearch	2005
publishDateSort	2005
publisher	Springer
record_format	marc
series2	Probability and its applications
spelling	Costa, O. L. Verfasser aut Discrete time Markov jump linear systems O. L. Costa ; M. D. Fragoso ; R. P. Marques 1. ed. London Springer 2005 X, 280 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probability and its applications Stochastische Kontrolltheorie (DE-588)4263657-7 gnd rswk-swf Sprungprozess (DE-588)4427906-1 gnd rswk-swf Markov-Sprungprozess (DE-588)4427907-3 gnd rswk-swf Diskreter Markov-Prozess (DE-588)4150185-8 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 s Sprungprozess (DE-588)4427906-1 s Diskreter Markov-Prozess (DE-588)4150185-8 s DE-604 Markov-Sprungprozess (DE-588)4427907-3 s 1\p DE-604 Fragoso, M. D. Verfasser aut Marques, R. P. Verfasser aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017440301&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Costa, O. L. Fragoso, M. D. Marques, R. P. Discrete time Markov jump linear systems Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Sprungprozess (DE-588)4427906-1 gnd Markov-Sprungprozess (DE-588)4427907-3 gnd Diskreter Markov-Prozess (DE-588)4150185-8 gnd
subject_GND	(DE-588)4263657-7 (DE-588)4427906-1 (DE-588)4427907-3 (DE-588)4150185-8
title	Discrete time Markov jump linear systems
title_auth	Discrete time Markov jump linear systems
title_exact_search	Discrete time Markov jump linear systems
title_full	Discrete time Markov jump linear systems O. L. Costa ; M. D. Fragoso ; R. P. Marques
title_fullStr	Discrete time Markov jump linear systems O. L. Costa ; M. D. Fragoso ; R. P. Marques
title_full_unstemmed	Discrete time Markov jump linear systems O. L. Costa ; M. D. Fragoso ; R. P. Marques
title_short	Discrete time Markov jump linear systems
title_sort	discrete time markov jump linear systems
topic	Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Sprungprozess (DE-588)4427906-1 gnd Markov-Sprungprozess (DE-588)4427907-3 gnd Diskreter Markov-Prozess (DE-588)4150185-8 gnd
topic_facet	Stochastische Kontrolltheorie Sprungprozess Markov-Sprungprozess Diskreter Markov-Prozess
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017440301&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT costaol discretetimemarkovjumplinearsystems AT fragosomd discretetimemarkovjumplinearsystems AT marquesrp discretetimemarkovjumplinearsystems

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