Exact and approximate modeling of linear systems: a behavioral approach
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
Society for Industrial and Applied Mathematics
2006
|
| Schriftenreihe: | Mathematical modeling and computation
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 197-202) and index |
| Beschreibung: | X, 206 S. Ill., graph. Darst. |
| ISBN: | 0898716039 |
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| 650 | 4 | |a Linear systems |x Mathematical models | |
| 650 | 4 | |a Approximation theory | |
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Datensatz im Suchindex
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| adam_text | EXACT AND APPROXIMATE MODELING OF LINEAR SYSTEMS A BEHAVIORAL APPROACH
IVAN MARKOVSKY JAN * WILLEMS SABINE VAN HUFFEL BART DE MOOR KATHOLIEKE
UNIVERSITEIT LEUVEN LEUVEN, BELGIUM 5JLEUTL SOCIETY FOR INDUSTRIAL AND
APPLIED MATHEMATICS PHILADELPHIA CONTENTS PREFACE IX 1 INTRODUCTION 1 1
.1 LATENCY AND MISFIT 1 1.2 DATA FITTING EXAMPLES 2 1.3 CLASSICAL VS.
BEHAVIORAL AND STOCHASTIC VS. DETERMINISTIC MODELING ... 9 1.4
CHAPTER-BY-CHAPTER OVERVIEW* 10 2 APPROXIMATE MODELING VIA MISFIT
MINIMIZATION 15 2.1 DATA, MODEL, MODEL CLASS, AND EXACT MODELING 15 2.2
MISFIT AND APPROXIMATE MODELING 17 2.3 MODEL REPRESENTATION AND
PARAMETERIZATION 18 2.4 LINEAR STATIC MODELS AND TOTAL LEAST SQUARES 19
2.5 NONLINEAR STATIC MODELS AND ELLIPSOID FITTING 21 2.6 DYNAMIC MODELS
AND GLOBAL TOTAL LEAST SQUARES 23 2.7 STRUCTURED TOTAL LEAST SQUARES 24
2.8 ALGORITHMS 25 I STATIC PROBLEMS 27 3 WEIGHTED TOTAL LEAST SQUARES 29
3.1 INTRODUCTION 29 3.2 KERNEL, IMAGE, AND INPUT/OUTPUT REPRESENTATIONS
33 3.3 SPECIAL CASES WITH CLOSED FORM SOLUTIONS 35 3.4 MISFIT
COMPUTATION 38 3.5 MISFIT MINIMIZATION* 40 3.6 SIMULATION EXAMPLES 46
3.7 CONCLUSIONS 47 4 STRUCTURED TOTAL LEAST SQUARES 49 4. 1 OVERVIEW OF
THE LITERATURE 49 4.2 THE STRUCTURED TOTAL LEAST SQUARES PROBLEM 51 4.3
PROPERTIES OF THE WEIGHT MATRIX* 54 4.4 STOCHASTIC INTERPRETATION* 58
4.5 EFFICIENT COST FUNCTION AND FIRST DERIVATIVE EVALUATION* 60 V VI
CONTENTS 4.6 SIMULATION EXAMPLES 64 4.7 CONCLUSIONS 68 5 BILINEAR
ERRORS-IN-VARIABLES MODEL 69 5.1 INTRODUCTION 69 5.2 ADJUSTED LEAST
SQUARES ESTIMATION OF A BILINEAR MODEL 70 5.3 PROPERTIES OF THE ADJUSTED
LEAST SQUARES ESTIMATOR* 72 5.4 SIMULATION EXAMPLES 74 5.5 FUNDAMENTAL
MATRIX ESTIMATION 75 5.6 ADJUSTED LEAST SQUARES ESTIMATION OF THE
FUNDAMENTAL MATRIX 77 5.7 PROPERTIES OF THE FUNDAMENTAL MATRIX
ESTIMATOR* 79 5.8 SIMULATION EXAMPLES 80 5.9 CONCLUSIONS 80 6 ELLIPSOID
FITTING 83 6.1 INTRODUCTION 83 6.2 QUADRATIC ERRORS-IN-VARIABLES MODEL
85 6.3 ORDINARY LEAST SQUARES ESTIMATION 86 6.4 ADJUSTED LEAST SQUARES
ESTIMATION 88 6.5 ELLIPSOID ESTIMATION 91 6.6 ALGORITHM FOR ADJUSTED
LEAST SQUARES ESTIMATION* 92 6.7 SIMULATION EXAMPLES 94 6.8 CONCLUSIONS
96 II DYNAMIC PROBLEMS 97 7 INTRODUCTION TO DYNAMICAL MODELS 99 7.1
LINEAR TIME-INVARIANT SYSTEMS 99 7.2 KERNEL REPRESENTATION 101 7.3
INPUTS, OUTPUTS, AND INPUT/OUTPUT REPRESENTATION 103 7.4 LATENT
VARIABLES, STATE VARIABLES, AND STATE SPACE REPRESENTATIONS .... 104 7.5
AUTONOMOUS AND CONTROLLABLE SYSTEMS 105 7.6 REPRESENTATIONS FOR
CONTROLLABLE SYSTEMS 106 7.7 REPRESENTATION THEOREM 107 7.8
PARAMETERIZATION OF A TRAJECTORY 109 7.9 COMPLEXITY OF A LINEAR
TIME-INVARIANT SYSTEM 110 7.10 THE MODULE OF ANNIHILATORS OF THE
BEHAVIOR* ILL 8 EXACT IDENTIFICATION 113 8.1 INTRODUCTION 113 8.2 THE
MOST POWERFUL UNFALSIFIED MODEL 115 8.3 IDENTIFIABILITY 117 8.4
CONDITIONS FOR IDENTIFIABILITY 118 8.5 ALGORITHMS FOR EXACT
IDENTIFICATION 120 8.6 COMPUTATION OF THE IMPULSE RESPONSE FROM DATA 124
8.7 REALIZATION THEORY AND ALGORITHMS 128 8.8 COMPUTATION OF FREE
RESPONSES 130 CONTENTS VII 8.9 RELATION TO SUBSPACE IDENTIFICATION
METHODS* 131 8.10 SIMULATION EXAMPLES 134 8.11 CONCLUSIONS 137 9
BALANCED MODEL IDENTIFICATION 139 9.1 INTRODUCTION 139 9.2 ALGORITHM FOR
BALANCED IDENTIFICATION 142 9.3 ALTERNATIVE ALGORITHMS 143 9.4 SPLITTING
OF THE DATA INTO PAST AND FUTURE * 144 9.5 SIMULATION EXAMPLES 145
9.6 CONCLUSIONS 147 10 ERRORS-IN-VARIABLES SMOOTHING AND FILTERING 149
10.1 INTRODUCTION 149 10.2 PROBLEM FORMULATION 150 10.3 SOLUTION OF THE
SMOOTHING PROBLEM 151 10.4 SOLUTION OF THE FILTERING PROBLEM 153 10.5
SIMULATION EXAMPLES 155 10.6 CONCLUSIONS 156 11 APPROXIMATE SYSTEM
IDENTIFICATION 157 11.1 APPROXIMATE MODELING PROBLEMS 157 11.2
APPROXIMATE IDENTIFICATION BY STRUCTURED TOTAL LEAST SQUARES 160 11.3
MODIFICATIONS OF THE BASIC PROBLEM 163 11.4 SPECIAL PROBLEMS 165 11.5
PERFORMANCE ON REAL-LIFE DATA SETS 169 11.6 CONCLUSIONS 172 12
CONCLUSIONS 175 A PROOFS 177 A.L WEIGHTED TOTAL LEAST SQUARES COST
FUNCTION GRADIENT 177 A.2 STRUCTURED TOTAL LEAST SQUARES COST FUNCTION
GRADIENT 178 A.3 FUNDAMENTAL LEMMA 179 A.4 RECURSIVE ERRORS-IN-VARIABLES
SMOOTHING 180 * SOFTWARE 183 B.L WEIGHTED TOTAL LEAST SQUARES 183 B.2
STRUCTURED TOTAL LEAST SQUARES 187 B.3 BALANCED MODEL IDENTIFICATION 190
B.4 APPROXIMATE IDENTIFICATION 190 NOTATION 195 BIBLIOGRAPHY 197 INDEX
203
|
| adam_txt |
EXACT AND APPROXIMATE MODELING OF LINEAR SYSTEMS A BEHAVIORAL APPROACH
IVAN MARKOVSKY JAN * WILLEMS SABINE VAN HUFFEL BART DE MOOR KATHOLIEKE
UNIVERSITEIT LEUVEN LEUVEN, BELGIUM 5JLEUTL SOCIETY FOR INDUSTRIAL AND
APPLIED MATHEMATICS PHILADELPHIA CONTENTS PREFACE IX 1 INTRODUCTION 1 1
.1 LATENCY AND MISFIT 1 1.2 DATA FITTING EXAMPLES 2 1.3 CLASSICAL VS.
BEHAVIORAL AND STOCHASTIC VS. DETERMINISTIC MODELING . 9 1.4
CHAPTER-BY-CHAPTER OVERVIEW* 10 2 APPROXIMATE MODELING VIA MISFIT
MINIMIZATION 15 2.1 DATA, MODEL, MODEL CLASS, AND EXACT MODELING 15 2.2
MISFIT AND APPROXIMATE MODELING 17 2.3 MODEL REPRESENTATION AND
PARAMETERIZATION 18 2.4 LINEAR STATIC MODELS AND TOTAL LEAST SQUARES 19
2.5 NONLINEAR STATIC MODELS AND ELLIPSOID FITTING 21 2.6 DYNAMIC MODELS
AND GLOBAL TOTAL LEAST SQUARES 23 2.7 STRUCTURED TOTAL LEAST SQUARES 24
2.8 ALGORITHMS 25 I STATIC PROBLEMS 27 3 WEIGHTED TOTAL LEAST SQUARES 29
3.1 INTRODUCTION 29 3.2 KERNEL, IMAGE, AND INPUT/OUTPUT REPRESENTATIONS
33 3.3 SPECIAL CASES WITH CLOSED FORM SOLUTIONS 35 3.4 MISFIT
COMPUTATION 38 3.5 MISFIT MINIMIZATION* 40 3.6 SIMULATION EXAMPLES 46
3.7 CONCLUSIONS 47 4 STRUCTURED TOTAL LEAST SQUARES 49 4. 1 OVERVIEW OF
THE LITERATURE 49 4.2 THE STRUCTURED TOTAL LEAST SQUARES PROBLEM 51 4.3
PROPERTIES OF THE WEIGHT MATRIX* 54 4.4 STOCHASTIC INTERPRETATION* 58
4.5 EFFICIENT COST FUNCTION AND FIRST DERIVATIVE EVALUATION* 60 V VI
CONTENTS 4.6 SIMULATION EXAMPLES 64 4.7 CONCLUSIONS 68 5 BILINEAR
ERRORS-IN-VARIABLES MODEL 69 5.1 INTRODUCTION 69 5.2 ADJUSTED LEAST
SQUARES ESTIMATION OF A BILINEAR MODEL 70 5.3 PROPERTIES OF THE ADJUSTED
LEAST SQUARES ESTIMATOR* 72 5.4 SIMULATION EXAMPLES 74 5.5 FUNDAMENTAL
MATRIX ESTIMATION 75 5.6 ADJUSTED LEAST SQUARES ESTIMATION OF THE
FUNDAMENTAL MATRIX 77 5.7 PROPERTIES OF THE FUNDAMENTAL MATRIX
ESTIMATOR* 79 5.8 SIMULATION EXAMPLES 80 5.9 CONCLUSIONS 80 6 ELLIPSOID
FITTING 83 6.1 INTRODUCTION 83 6.2 QUADRATIC ERRORS-IN-VARIABLES MODEL
85 6.3 ORDINARY LEAST SQUARES ESTIMATION 86 6.4 ADJUSTED LEAST SQUARES
ESTIMATION 88 6.5 ELLIPSOID ESTIMATION 91 6.6 ALGORITHM FOR ADJUSTED
LEAST SQUARES ESTIMATION* 92 6.7 SIMULATION EXAMPLES 94 6.8 CONCLUSIONS
96 II DYNAMIC PROBLEMS 97 7 INTRODUCTION TO DYNAMICAL MODELS 99 7.1
LINEAR TIME-INVARIANT SYSTEMS 99 7.2 KERNEL REPRESENTATION 101 7.3
INPUTS, OUTPUTS, AND INPUT/OUTPUT REPRESENTATION 103 7.4 LATENT
VARIABLES, STATE VARIABLES, AND STATE SPACE REPRESENTATIONS . 104 7.5
AUTONOMOUS AND CONTROLLABLE SYSTEMS 105 7.6 REPRESENTATIONS FOR
CONTROLLABLE SYSTEMS 106 7.7 REPRESENTATION THEOREM 107 7.8
PARAMETERIZATION OF A TRAJECTORY 109 7.9 COMPLEXITY OF A LINEAR
TIME-INVARIANT SYSTEM 110 7.10 THE MODULE OF ANNIHILATORS OF THE
BEHAVIOR* ILL 8 EXACT IDENTIFICATION 113 8.1 INTRODUCTION 113 8.2 THE
MOST POWERFUL UNFALSIFIED MODEL 115 8.3 IDENTIFIABILITY 117 8.4
CONDITIONS FOR IDENTIFIABILITY 118 8.5 ALGORITHMS FOR EXACT
IDENTIFICATION 120 8.6 COMPUTATION OF THE IMPULSE RESPONSE FROM DATA 124
8.7 REALIZATION THEORY AND ALGORITHMS 128 8.8 COMPUTATION OF FREE
RESPONSES 130 CONTENTS VII 8.9 RELATION TO SUBSPACE IDENTIFICATION
METHODS* 131 8.10 SIMULATION EXAMPLES 134 8.11 CONCLUSIONS 137 9
BALANCED MODEL IDENTIFICATION 139 9.1 INTRODUCTION 139 9.2 ALGORITHM FOR
BALANCED IDENTIFICATION 142 9.3 ALTERNATIVE ALGORITHMS 143 9.4 SPLITTING
OF THE DATA INTO "PAST" AND "FUTURE"* 144 9.5 SIMULATION EXAMPLES 145
9.6 CONCLUSIONS 147 10 ERRORS-IN-VARIABLES SMOOTHING AND FILTERING 149
10.1 INTRODUCTION 149 10.2 PROBLEM FORMULATION 150 10.3 SOLUTION OF THE
SMOOTHING PROBLEM 151 10.4 SOLUTION OF THE FILTERING PROBLEM 153 10.5
SIMULATION EXAMPLES 155 10.6 CONCLUSIONS 156 11 APPROXIMATE SYSTEM
IDENTIFICATION 157 11.1 APPROXIMATE MODELING PROBLEMS 157 11.2
APPROXIMATE IDENTIFICATION BY STRUCTURED TOTAL LEAST SQUARES 160 11.3
MODIFICATIONS OF THE BASIC PROBLEM 163 11.4 SPECIAL PROBLEMS 165 11.5
PERFORMANCE ON REAL-LIFE DATA SETS 169 11.6 CONCLUSIONS 172 12
CONCLUSIONS 175 A PROOFS 177 A.L WEIGHTED TOTAL LEAST SQUARES COST
FUNCTION GRADIENT 177 A.2 STRUCTURED TOTAL LEAST SQUARES COST FUNCTION
GRADIENT 178 A.3 FUNDAMENTAL LEMMA 179 A.4 RECURSIVE ERRORS-IN-VARIABLES
SMOOTHING 180 * SOFTWARE 183 B.L WEIGHTED TOTAL LEAST SQUARES 183 B.2
STRUCTURED TOTAL LEAST SQUARES 187 B.3 BALANCED MODEL IDENTIFICATION 190
B.4 APPROXIMATE IDENTIFICATION 190 NOTATION 195 BIBLIOGRAPHY 197 INDEX
203 |
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| index_date | 2024-07-02T17:22:23Z |
| indexdate | 2024-07-09T20:57:01Z |
| institution | BVB |
| isbn | 0898716039 |
| language | English |
| lccn | 2005057537 |
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| publisher | Society for Industrial and Applied Mathematics |
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| series2 | Mathematical modeling and computation |
| spelling | Exact and approximate modeling of linear systems a behavioral approach Ivan Markovsky ... [et al.] Philadelphia Society for Industrial and Applied Mathematics 2006 X, 206 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical modeling and computation Includes bibliographical references (p. 197-202) and index Mathematisches Modell Linear systems Mathematical models Approximation theory Mathematical statistics Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Lineares stochastisches System (DE-588)4167737-7 gnd rswk-swf Lineares stochastisches System (DE-588)4167737-7 s Approximationstheorie (DE-588)4120913-8 s DE-604 Markovsky, Ivan Sonstige oth http://www.loc.gov/catdir/enhancements/fy0708/2005057537-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0708/2005057537-t.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015620334&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Exact and approximate modeling of linear systems a behavioral approach Mathematisches Modell Linear systems Mathematical models Approximation theory Mathematical statistics Approximationstheorie (DE-588)4120913-8 gnd Lineares stochastisches System (DE-588)4167737-7 gnd |
| subject_GND | (DE-588)4120913-8 (DE-588)4167737-7 |
| title | Exact and approximate modeling of linear systems a behavioral approach |
| title_auth | Exact and approximate modeling of linear systems a behavioral approach |
| title_exact_search | Exact and approximate modeling of linear systems a behavioral approach |
| title_exact_search_txtP | Exact and approximate modeling of linear systems a behavioral approach |
| title_full | Exact and approximate modeling of linear systems a behavioral approach Ivan Markovsky ... [et al.] |
| title_fullStr | Exact and approximate modeling of linear systems a behavioral approach Ivan Markovsky ... [et al.] |
| title_full_unstemmed | Exact and approximate modeling of linear systems a behavioral approach Ivan Markovsky ... [et al.] |
| title_short | Exact and approximate modeling of linear systems |
| title_sort | exact and approximate modeling of linear systems a behavioral approach |
| title_sub | a behavioral approach |
| topic | Mathematisches Modell Linear systems Mathematical models Approximation theory Mathematical statistics Approximationstheorie (DE-588)4120913-8 gnd Lineares stochastisches System (DE-588)4167737-7 gnd |
| topic_facet | Mathematisches Modell Linear systems Mathematical models Approximation theory Mathematical statistics Approximationstheorie Lineares stochastisches System |
| url | http://www.loc.gov/catdir/enhancements/fy0708/2005057537-d.html http://www.loc.gov/catdir/enhancements/fy0708/2005057537-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015620334&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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