Adaptive systems: an introduction
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1996
|
| Series: | Systems & control
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 339 S. |
| ISBN: | 0817638776 3764338776 |
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Record in the Search Index
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| adam_text | Contents
Preface xiii
Acknowledgements xvi
1 Adaptive Systems 1
1.1 Introduction 1
1.2 Adaptive systems: examples 1
1.2.1 Adaptive control 1
1.2.2 Adaptive signal processing 3
1.2.3 Adaptive systems versus classical techniques 3
1.3 General structure of adaptive control systems 4
1.3.1 Introduction 4
1.3.2 The general structure 4
1.3.3 The error signal 8
1.3.4 The tuner 9
1.3.5 Certainty equivalence 11
1.3.6 Design and analysis 12
1.4 Illustrating the concepts 13
1.4.1 The MIT rule for adaptive control: feedforward case ... 13
1.4.2 The MIT rule for adaptive control: feedback problem . . . 16
1.4.3 An adaptive pole placement scheme 19
1.4.4 A universal controller 21
1.4.5 Echo cancelling 22
1.5 Summary of chapter 25
1.6 Notes and references 25
1.7 Exercises 25
vi Contents
2 Systems And Their Representations 27
2.1 Introduction 27
2.2 Notation 28
2.3 The behavior 28
2.4 Latent variables 31
2.5 Equivalent representations 32
2.6 Controllability 33
2.7 Observability 35
2.8 Stability 37
2.9 Elimination of Latent variables 39
2.10 The ring Rt^.r1] 43
2.11 An example 47
2.12 A word about the notation 48
2.13 Summary of chapter 49
2.14 Notes and references 49
3 Adaptive systems : principles of identification 50
3.1 Introduction 50
3.2 Object of interest and model class 51
3.2.1 Object of interest 51
3.2.2 Model class 53
3.3 Identification criterion and algorithms 58
3.3.1 Least squares identification 58
3.3.2 Recursive Least Squares (RLS) 59
3.3.3 Projection algorithm 63
3.3.3.1 Basic projection algorithm 63
3.3.3.2 Normalized Least Mean Square (NLMS) .... 64
3.3.3.3 Projection with dead zone 65
3.3.3.4 Least Mean Square Algorithm (LMS) 66
3.4 Data model assumptions 67
3.4.1 Stable data filter 67
3.4.2 Data in model class 67
3.4.3 Information content of data 69
3.4.4 Data do not fit model class 70
3.5 Analysis of identification algorithms 71
3.5.1 Properties of recursive least squares 71
Contents vii
3.5.1.1 Consistency for RLS 74
3.5.1.2 Consistency with model errors for RLS 76
3.5.2 Properties of the NLMS algorithm 78
3.5.2.1 With NLMS the equation error converges . ... 78
3.5.2.2 Consistency for NLMS 80
3.5.2.3 Consistency with model errors for NLMS ... 82
3.5.3 Projection algorithm with dead zone 84
3.5.4 Tracking properties 86
3.5.4.1 NLMS algorithm can track 87
3.5.4.2 RLS algorithm cannot track 88
3.5.5 Incorporating prior knowledge in algorithms 91
3.6 Persistency of excitation 91
3.7 Summary of chapter 96
3.8 Notes and references 96
3.9 Exercises 97
4 Adaptive Pole Assignment 103
4.1 Introduction 103
4.2 Preliminaries 105
4.3 The system and its representations 107
4.4 Equilibrium analysis 109
4.4.1 The error model 110
4.4.2 How much can be learned,
and how much must be learned? 110
4.5 An algorithm for adaptive pole assignment 114
4.5.1 The adaptive system 114
4.6 Analysis of the algorithm 117
4.6.1 Nonminimal representation 118
4.6.2 Minimal representation 120
4.7 Filtered signals 124
4.7.1 Filter representation of i/o systems 124
4.7.2 Application to adaptive pole assignment 128
4.8 Modification of the projection algorithm 133
4.9 Summary of chapter 135
4.10 Notes and references 135
4.11 Exercises 136
viii Contents
5 Direct Adaptive Model Reference Control 139
5.1 Introduction 139
5.2 Basic problem definition 140
5.3 Model reference control: nonadaptive solution 142
5.4 Error model construction 147
5.5 Equilibrium analysis 152
5.6 Adaptive algorithm 155
5.6.1 Adaptive model reference control algorithm 155
5.7 Analysis of the adaptive system 156
5.7.1 Stability of the adaptive system 157
5.7.2 Parameter convergence? 162
5.8 Adaptive model reference control with
disturbance rejection 164
5.8.1 The Internal Model Principle 164
5.8.2 Model reference control with disturbance rejection .... 167
5.8.3 Adaptive model reference control with
known disturbance rejection 168
5.8.4 Adaptive model reference and disturbance rejection control 169
5.9 Summary of chapter 169
5.10 Notes and references 170
5.11 Exercises 171
6 Universal Controllers 172
6.1 Introduction 172
6.2 Existence of solutions 174
6.3 The first order case 174
6.3.1 Sign b known 175
6.3.2 The Nussbaum controller: sign b unknown 178
6.3.3 The Willems Byrnes controller: sign b unknown .... 183
6.4 Higher order systems 185
6.4.1 High gain feedback 186
6.4.2 Willems Byrnes controller: sign of qn^ known 189
6.4.3 Willems Byrnes controller: sign qn_ unknown 190
6.5 Martensson s algorithm 193
6.5.1 The adaptive control problem 194
6.5.2 The main result 195
6.5.3 Dense curves 197
Contents ix
6.5.4 A dense curve based on an enumeration of QN 198
6.6 Summary of chapter 198
6.7 Notes and references 199
6.8 Exercises 199
7 The pole/zero cancellation problem 204
7.1 Introduction 204
7.2 The pole/zero cancellation problem in adaptive control 205
7.3 Combining direct and indirect adaptive control 207
7.3.1 The first order case 207
7.3.1.1 Problem statement and reparametrization .... 207
7.3.1.2 Equilibrium analysis 208
7.3.1.3 Adaptive algorithm 209
7.3.2 The higher order case 210
7.3.2.1 Problem statement and reparametrization .... 210
7.3.2.2 Equilibrium analysis 212
7.3.2.3 Adaptive algorithm 218
7.4 Adaptive Excitation 219
7.4.1 The first order case 220
7.4.1.1 Problem statement 220
7.4.1.2 Adaptive algorithm 220
7.4.2 The higher order case 223
7.4.2.1 Problem statement 223
7.4.2.2 Adaptive algorithm 223
7.5 A more fundamental viewpoint 225
7.5.1 The connection with tunability 226
7.5.2 Alternative parametrizations 227
7.6 Conclusions 228
7.7 Summary of chapter 228
7.8 Notes and references 228
7.9 Exercises 230
8 Averaging Analysis For Adaptive Systems 232
8.1 Introduction 232
8.2 Averaging 233
8.2.1 An illustration 235
8.2.2 Some notation and preliminaries 239
x Contents
8.2.3 Finite horizon averaging result 241
8.2.4 Infinite horizon result 244
8.3 Transforming an adaptive system into standard form 251
8.4 Averaging approximation 258
8.5 Application: the MIT rule for adaptive control 260
8.5.1 System description 260
8.5.2 Frozen system for MIT rule 261
8.5.3 Averaging for MIT rule 261
8.5.4 Interpretation of averaged system 263
8.5.4.1 Case I: Reference model equals plant Zm = Zv . 263
8.5.4.2 Case II: Constant reference signal 263
8.5.4.3 Case III: General problem 264
8.5.4.4 How slow is slow adaptation? 266
8.6 Application: echo cancellation in telephony 267
8.6.1 Echo cancellation 267
8.6.2 System description and assumptions 268
8.6.3 Analysis 271
8.6.3.1 The frozen system 271
8.6.3.2 The averaged update equation 272
8.6.3.3 Analysis of the averaged equation 274
8.6.3.4 DEC system behavior 277
8.6.3.5 General observations 279
8.7 Summary of chapter 280
8.8 Notes and references 281
8.9 Exercises 282
9 Dynamics of adaptive systems: A case study 286
9.1 Introduction 286
9.2 The example 287
9.3 Global analysis and bifurcations 289
9.4 Adaptive system behavior: ideal case 291
9.5 Adaptive system behavior: undermodelled case 294
9.5.1 Parameter range 296
9.5.2 Equilibria 296
9.5.3 Beyond period 1 bifurcations 298
9.5.4 Summary d # 0 299
Contents xi
9.5.5 Flip bifurcation revisited 300
9.6 Discussion 301
9.7 Summary of chapter 302
9.8 Notes and References 303
9.9 Exercises 303
Epilogue 304
A Background material 305
A.I A contraction result 305
A.2 The Comparison Principle 306
A.2.1 Bellman Gronwall Lemma 307
A.2.2 Perturbed linear stable systems 308
A.3 Miscellaneous stability results 311
A.3.1 Stability Definitions 311
A.3.2 Some Lyapunov stability results 312
A.4 Detectability 313
A.5 An inequality for linear systems 317
A.6 Finite horizon averaging result 319
A.7 Maple code for solving Lyapunov equations 324
A.8 Maple code for fixed points and two periodic solutions 325
Bibliography 327
Index 336
|
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| spelling | Mareels, Iven Verfasser aut Adaptive systems an introduction Iven Mareels ; Jan Willem Polderman Boston [u.a.] Birkhäuser 1996 XVII, 339 S. txt rdacontent n rdamedia nc rdacarrier Systems & control Teoria de sistemas adaptativos larpcal Adaptive control systems Adaptives System (DE-588)4247928-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Adaptives System (DE-588)4247928-9 s DE-604 Polderman, Jan Willem 1956- Verfasser (DE-588)114680418 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007349515&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mareels, Iven Polderman, Jan Willem 1956- Adaptive systems an introduction Teoria de sistemas adaptativos larpcal Adaptive control systems Adaptives System (DE-588)4247928-9 gnd |
| subject_GND | (DE-588)4247928-9 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Adaptive systems an introduction |
| title_auth | Adaptive systems an introduction |
| title_exact_search | Adaptive systems an introduction |
| title_full | Adaptive systems an introduction Iven Mareels ; Jan Willem Polderman |
| title_fullStr | Adaptive systems an introduction Iven Mareels ; Jan Willem Polderman |
| title_full_unstemmed | Adaptive systems an introduction Iven Mareels ; Jan Willem Polderman |
| title_short | Adaptive systems |
| title_sort | adaptive systems an introduction |
| title_sub | an introduction |
| topic | Teoria de sistemas adaptativos larpcal Adaptive control systems Adaptives System (DE-588)4247928-9 gnd |
| topic_facet | Teoria de sistemas adaptativos Adaptive control systems Adaptives System Einführung Lehrbuch |
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