System identification with quantized observations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2010
|
| Edition: | 1., Auflage |
| Series: | Systems & Control: Foundations & Applications
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 317 S. graph. Darst. |
| ISBN: | 9780817649555 |
Staff View
MARC
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| 016 | 7 | |a 611235900 |2 DE-101 | |
| 020 | |a 9780817649555 |9 978-0-8176-4955-5 | ||
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| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
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| 084 | |a SK 880 |0 (DE-625)143266: |2 rvk | ||
| 100 | 1 | |a Wang, Le Yi |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a System identification with quantized observations |c Le Yi Wang ; G. George Yin ; Ji-Feng Zhang ; Yanlong Zhao |
| 250 | |a 1., Auflage | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2010 | |
| 300 | |a XVIII, 317 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Systems & Control: Foundations & Applications | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020195180 | ||
Record in the Search Index
| _version_ | 1804142782994972672 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE XIII
CONVENTIONS XV
GLOSSARY OF SYMBOLS XVII
PART I: OVERVIEW 1
1 INTRODUCTION 3
1.1 MOTIVATING EXAMPLES . . . . . . . . . . . . . . . . . . . . . . 4
1.2 SYSTEM IDENTIFICATION WITH QUANTIZED OBSERVATIONS . . . . . 7 1.3
OUTLINE OF THE BOOK . . . . . . . . . . . . . . . . . . . . . . 8
2 SYSTEM SETTINGS 13
2.1 BASIC SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 QUANTIZED OUTPUT OBSERVATIONS . . . . . . . . . . . . . . . . 16
2.3 INPUTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.4 SYSTEM CONFIGURATIONS . . . . . . . . . . . . . . . . . . . . . 18
2.4.1 FILTERING AND FEEDBACK CONFIGURATIONS . . . . . . . . 19
2.4.2 SYSTEMS WITH COMMUNICATION CHANNELS . . . . . . . 19
2.5 UNCERTAINTIES . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.1 SYSTEM UNCERTAINTIES: UNMODELED DYNAMICS . . . . 20 2.5.2 SYSTEM
UNCERTAINTIES: FUNCTION MISMATCH . . . . . . 21 2.5.3 SENSOR BIAS AND
DRIFTS . . . . . . . . . . . . . . . . . 21
2.5.4 NOISE . . . . . . . . . . . . . . . . . . . . . . . . . . 21
IMAGE 2
VIII CONTENTS
2.5.5 UNKNOWN NOISE CHARACTERISTICS . . . . . . . . . . . . 22
2.5.6 COMMUNICATION CHANNEL UNCERTAINTIES . . . . . . . . 22
2.6 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
PART II: STOCHASTIC METHODS FOR LINEAR SYSTEMS 23
3 EMPIRICAL-MEASURE-BASED IDENTIFICATION 25
3.1 AN OVERVIEW OF EMPIRICAL-MEASURE-BASED IDENTIFICATION . . 26 3.2
EMPIRICAL MEASURES AND IDENTIFICATION ALGORITHMS . . . . . 29 3.3 STRONG
CONVERGENCE . . . . . . . . . . . . . . . . . . . . . . 32
3.4 ASYMPTOTIC DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . 34
3.5 MEAN-SQUARE CONVERGENCE . . . . . . . . . . . . . . . . . . . 37
3.6 CONVERGENCE UNDER DEPENDENT NOISE . . . . . . . . . . . . . 41
3.7 PROOFS OF TWO PROPOSITIONS . . . . . . . . . . . . . . . . . . 43
3.8 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 ESTIMATION ERROR BOUNDS: INCLUDING UNMODELED DYNAMICS 49 4.1
WORST-CASE PROBABILISTIC ERRORS AND TIME COMPLEXITY . . . 50 4.2 UPPER
BOUNDS ON ESTIMATION ERRORS AND TIME COMPLEXITY 50 4.3 LOWER BOUNDS ON
ESTIMATION ERRORS . . . . . . . . . . . . . 53
4.4 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 RATIONAL SYSTEMS 59
5.1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 ESTIMATION OF X K . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 ESTIMATION OF PARAMETER * . . . . . . . . . . . . . . . . . . . 62
5.3.1 PARAMETER IDENTIFIABILITY . . . . . . . . . . . . . . . . 62
5.3.2 IDENTIFICATION ALGORITHMS AND CONVERGENCE ANALYSIS 65 5.4 NOTES .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6 QUANTIZED IDENTIFICATION AND ASYMPTOTIC EFFICIENCY 67 6.1 BASIC
ALGORITHMS AND CONVERGENCE . . . . . . . . . . . . . . 68
6.2 QUASI-CONVEX COMBINATION ESTIMATORS (QCCE) . . . . . . 70 6.3
ALTERNATIVE COVARIANCE EXPRESSIONS OF OPTIMAL QCCES . . . 72 6.4 CRAM´
ER-RAO LOWER BOUNDS AND ASYMPTOTIC EFFICIENCY OF THE OPTIMAL QCCE . . .
. . . . . . . . . . . . . . . . . . . . 75
6.5 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7 INPUT DESIGN FOR IDENTIFICATION IN CONNECTED SYSTEMS 81 7.1 INVARIANCE
OF INPUT PERIODICITY AND RANK IN OPEN- AND CLOSED-LOOP CONFIGURATIONS .
. . . . . . . . . . . . . . . . . . . . . 82
7.2 PERIODIC DITHERS . . . . . . . . . . . . . . . . . . . . . . . . 83
7.3 SUFFICIENT RICHNESS CONDITIONS UNDER INPUT NOISE . . . . . . 85 7.4
ACTUATOR NOISE . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.5 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
IMAGE 3
CONTENTS IX
8 IDENTIFICATION OF SENSOR THRESHOLDS AND NOISE DISTRIBUTION FUNCTIONS
95
8.1 IDENTIFICATION OF UNKNOWN THRESHOLDS . . . . . . . . . . . . 95
8.1.1 SUFFICIENT RICHNESS CONDITIONS . . . . . . . . . . . . . 96
8.1.2 RECURSIVE ALGORITHMS . . . . . . . . . . . . . . . . . 99
8.2 PARAMETERIZED DISTRIBUTION FUNCTIONS . . . . . . . . . . . . 99
8.3 JOINT IDENTIFICATION PROBLEMS . . . . . . . . . . . . . . . . . 101
8.4 RICHNESS CONDITIONS FOR JOINT IDENTIFICATION . . . . . . . . . 101
8.5 ALGORITHMS FOR IDENTIFYING SYSTEM PARAMETERS AND DISTRIBUTION
FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.6 CONVERGENCE ANALYSIS . . . . . . . . . . . . . . . . . . . . . 105
8.7 RECURSIVE ALGORITHMS . . . . . . . . . . . . . . . . . . . . . . 106
8.7.1 RECURSIVE SCHEMES . . . . . . . . . . . . . . . . . . . 107
8.7.2 ASYMPTOTIC PROPERTIES OF RECURSIVE ALGORITHM (8.14) 108 8.8
ALGORITHM FLOWCHARTS . . . . . . . . . . . . . . . . . . . . . 111
8.9 ILLUSTRATIVE EXAMPLES . . . . . . . . . . . . . . . . . . . . . .
113
8.10 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
115
PART III: DETERMINISTIC METHODS FOR LINEAR SYSTEMS 117
9 WORST-CASE IDENTIFICATION 119
9.1 WORST-CASE UNCERTAINTY MEASURES . . . . . . . . . . . . . . 120
9.2 LOWER BOUNDS ON IDENTIFICATION ERRORS AND TIME COMPLEXITY 121 9.3
UPPER BOUNDS ON TIME COMPLEXITY . . . . . . . . . . . . . 124
9.4 IDENTIFICATION OF GAINS . . . . . . . . . . . . . . . . . . . . .
127
9.5 IDENTIFICATION USING COMBINED DETERMINISTIC AND STOCHASTIC METHODS .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.5.1 IDENTIFIABILITY CONDITIONS AND PROPERTIES UNDER DETERMINISTIC AND
STOCHASTIC FRAMEWORKS . . . . . . . . 136
9.5.2 COMBINED DETERMINISTIC AND STOCHASTIC IDENTIFICATION METHODS . . .
. . . . . . . . . . . . . . . . . . . 139
9.5.3 OPTIMAL INPUT DESIGN AND CONVERGENCE SPEED UNDER TYPICAL
DISTRIBUTIONS . . . . . . . . . . . . . . . . . 141
9.6 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
145
10 WORST-CASE IDENTIFICATION USING QUANTIZED OBSERVATIONS 149 10.1
WORST-CASE IDENTIFICATION WITH QUANTIZED OBSERVATIONS . . . 150 10.2
INPUT DESIGN FOR PARAMETER DECOUPLING . . . . . . . . . . . 151
10.3 IDENTIFICATION OF SINGLE-PARAMETER SYSTEMS . . . . . . . . . . 153
10.3.1 GENERAL QUANTIZATION . . . . . . . . . . . . . . . . . 154
10.3.2 UNIFORM QUANTIZATION . . . . . . . . . . . . . . . . . 159
10.4 TIME COMPLEXITY . . . . . . . . . . . . . . . . . . . . . . . . 163
10.5 EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . .
165
10.6 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
168
IMAGE 4
X CONTENTS
PART IV: IDENTIFICATION OF NONLINEAR AND SWITCHING SYSTEMS 171
11 IDENTIFICATION OF WIENER SYSTEMS 173
11.1 WIENER SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . .
174
11.2 BASIC INPUT DESIGN AND CORE IDENTIFICATION PROBLEMS . . . . 175
11.3 PROPERTIES OF INPUTS AND SYSTEMS . . . . . . . . . . . . . . . 177
11.4 IDENTIFICATION ALGORITHMS . . . . . . . . . . . . . . . . . . . 179
11.5 ASYMPTOTIC EFFICIENCY OF THE CORE IDENTIFICATION ALGORITHMS 184
11.6 RECURSIVE ALGORITHMS AND CONVERGENCE . . . . . . . . . . . . 188
11.7 EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . .
190
11.8 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
194
12 IDENTIFICATION OF HAMMERSTEIN SYSTEMS 197
12.1 PROBLEM FORMULATION . . . . . . . . . . . . . . . . . . . . . . 198
12.2 INPUT DESIGN AND STRONG-FULL-RANK SIGNALS . . . . . . . . . 199
12.3 ESTIMATES OF * WITH INDIVIDUAL THRESHOLDS . . . . . . . . . . 202
12.4 QUASI-CONVEX COMBINATION ESTIMATORS OF * . . . . . . . . . 204
12.5 ESTIMATION OF SYSTEM PARAMETERS . . . . . . . . . . . . . . . 212
12.6 EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . .
218
12.7 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
222
13 SYSTEMS WITH MARKOVIAN PARAMETERS 225
13.1 MARKOV SWITCHING SYSTEMS WITH BINARY OBSERVATIONS . . . . 227 13.2
WONHAM-TYPE FILTERS . . . . . . . . . . . . . . . . . . . . . 227
13.3 TRACKING: MEAN-SQUARE CRITERIA . . . . . . . . . . . . . . . . 229
13.4 TRACKING INFREQUENTLY SWITCHING SYSTEMS: MAP METHODS . 237 13.5
TRACKING FAST-SWITCHING SYSTEMS . . . . . . . . . . . . . . . 242
13.5.1 LONG-RUN AVERAGE BEHAVIOR . . . . . . . . . . . . . . 243
13.5.2 EMPIRICAL MEASURE-BASED ESTIMATORS . . . . . . . . . 245
13.5.3 ESTIMATION ERRORS ON EMPIRICAL MEASURES: UPPER AND LOWER BOUNDS .
. . . . . . . . . . . . . . . . . . . . 249
13.6 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
252
PART V: COMPLEXITY ANALYSIS 253
14 COMPLEXITIES, THRESHOLD SELECTION, ADAPTATION 255 14.1 SPACE AND TIME
COMPLEXITIES . . . . . . . . . . . . . . . . . 256
14.2 BINARY SENSOR THRESHOLD SELECTION AND INPUT DESIGN . . . . 259 14.3
WORST-CASE OPTIMAL THRESHOLD DESIGN . . . . . . . . . . . . 261
14.4 THRESHOLD ADAPTATION . . . . . . . . . . . . . . . . . . . . . 264
14.5 QUANTIZED SENSORS AND OPTIMAL RESOURCE ALLOCATION . . . . 267 14.6
DISCUSSIONS ON SPACE AND TIME COMPLEXITY . . . . . . . . . 271
14.7 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
272
15 IMPACT OF COMMUNICATION CHANNELS 275
15.1 IDENTIFICATION WITH COMMUNICATION CHANNELS . . . . . . . . 276
IMAGE 5
CONTENTS XI
15.2 MONOTONICITY OF FISHER INFORMATION . . . . . . . . . . . . . . 277
15.3 FISHER INFORMATION RATIO OF COMMUNICATION CHANNELS . . . 278 15.4
VECTOR-VALUED PARAMETERS . . . . . . . . . . . . . . . . . . . 280
15.5 RELATIONSHIP TO SHANNON S MUTUAL INFORMATION . . . . . . . 282 15.6
TRADEOFF BETWEEN TIME INFORMATION AND SPACE INFORMATION 283 15.7
INTERCONNECTIONS OF COMMUNICATION CHANNELS . . . . . . . . 284 15.8
NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
A BACKGROUND MATERIALS 287
A.1 MARTINGALES . . . . . . . . . . . . . . . . . . . . . . . . . . .
287
A.2 MARKOV CHAINS . . . . . . . . . . . . . . . . . . . . . . . . . 290
A.3 WEAK CONVERGENCE . . . . . . . . . . . . . . . . . . . . . . . 299
A.4 MISCELLANY . . . . . . . . . . . . . . . . . . . . . . . . . . . .
302
REFERENCES 305
INDEX 315
|
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| spelling | Wang, Le Yi Verfasser aut System identification with quantized observations Le Yi Wang ; G. George Yin ; Ji-Feng Zhang ; Yanlong Zhao 1., Auflage Boston [u.a.] Birkhäuser 2010 XVIII, 317 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Systems & Control: Foundations & Applications SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195180&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wang, Le Yi System identification with quantized observations |
| title | System identification with quantized observations |
| title_auth | System identification with quantized observations |
| title_exact_search | System identification with quantized observations |
| title_full | System identification with quantized observations Le Yi Wang ; G. George Yin ; Ji-Feng Zhang ; Yanlong Zhao |
| title_fullStr | System identification with quantized observations Le Yi Wang ; G. George Yin ; Ji-Feng Zhang ; Yanlong Zhao |
| title_full_unstemmed | System identification with quantized observations Le Yi Wang ; G. George Yin ; Ji-Feng Zhang ; Yanlong Zhao |
| title_short | System identification with quantized observations |
| title_sort | system identification with quantized observations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195180&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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