Appropriate for courses in System Identification. This book is a comprehensive and coherent description of the theory, methodology and practice of System Identification-the science of building mathematical models of dynamic systems by observing input/output data. It puts the user in focus, giving the necessary background to understand theoretical foundation and emphasizing the practical aspects of the options and choices that face the user. The Second Edition has been updated to include material on subspace methods, non-linear black box models-such as neural networks-and methods that use frequency domain data.
Author(s): Lennart Ljung
Edition: 2nd Edition
Publisher: Prentice Hall
Year: 1999
Language: English
Pages: 672
Preface to the First Edition xiv
Acknowledgments xvi
Preface to the Second Edition xviii
Operators and Notational Conventions xix
• 1 Introduction 1
1.1 Dynamic Systems 1
1.2 Models 6
1.3 An Archetypical Problem—ARX Models and the Linear Least Squares
Method 8
1.4 The System Identification Procedure 13
1.5 Organization of the Book 14
1.6 Bibliography 16
part i: systems and models
• 2 Time-Invariant Linear Systems 18
2.1 Impulse Responses, Disturbances, and Transfer Functions 18
2.2 Frequency-Domain Expressions 28
2.3 Signal Spectra 33
2.4 Single Realization Behavior and Ergodicity Results (*) 42
2.5 Multivariable Systems (*) 44
2.6 Summary 45
2.7 Bibliography 46
2.8 Problems 47
Appendix 2A: Proof of Theorem 2.2 52
Appendix 2B: Proof of Theorem 2.3 55
Appendix 2C: Covariance Formulas 61
• 3 Simulation and Prediction 63
3.1 Simulation 63
3.2 Prediction 64
3.3 Observers 72
3.4 Summary 75
3.5 Bibliography 75
3.6 Problems 76
• 4 Models of Linear Time-Invariant Systems 79
4.1 Linear Models and Sets of Linear Models 79
4.2 A Family of Transfer-Function Models 81
4.3 State-Space Models 93
4.4 Distributed Parameter Models (*) 103
4.5 Model Sets. Model Structures, and Identifiabilitv: Some Formal Aspects
(*) 105
4.6 Identifiabilitv of Some Model Structures 114
4.7 Summary 118
4.8 Bibliography 119
4.9 Problems 121
Appendix 4A: Identifiabilitv of Black-Box Multivariable Model
Structures 128
• 5 Models for Time-varying and Nonlinear Systems 140
5.1 Linear Time-Varying Models 140
5.2 Models with Nonlinearities 143
5.3 Nonlinear State-Space Models 146
5.4 Nonlinear Black-Box Models: Basic Principles 148
5.5 Nonlinear Black-Box Models: Neural Networks, Wavelets and Classical
Models 154
5.6 Fuzzy Models 156
5.7 Formal Characterization of Models (*) 161
5.8 Summary 164
5.9 Bibliography 165
5.10 Problems 165
part ii: methods
• 6 Nonparametric Time- and Frequency-Domain Methods 168
6.1 Transient-Response Analysis and Correlation Analysis 168
6.2 Frequency-Response Analysis 170
6.3 Fourier Analysis 173
6.4 Spectral Analysis 178
6.5 Estimating the Disturbance Spectrum (*) 187
6.6 Summary 189
6.7 Bibliography 190
6.8 Problems 191
Appendix 6A: Derivation of the Asymptotic Properties of the Spectral
Analysis Estimate 194
• 7 Parameter Estimation Methods 197
7.1 Guiding Principles Behind Parameter Estimation Methods 197
7.2 Minimizing Prediction Errors 199
7.3 Linear Regressions and the Least-Squares Method 203
7.4 A Statistical Framework for Parameter Estimation and the Maximum
Likelihood Method 212
7.5 Correlating Prediction Errors with Past Data 222
7.6 Instrumental-Variable Methods 224
7.7 Using Frequency Domain Data to Fit Linear Models (*) 227
7.8 Summary 233
7.9 Bibliography 234
7.10 Problems 236
Appendix 7A: Proof of the Cramer-Rao Inequality 245
• 8 Convergence and Consistency 247
8.1 Introduction 247
8.2 Conditions on the Data Set 249
8.3 Prediction-Error Approach 253
8.4 Consistency and Identifiabilitv 258
8.5 Linear Time-Invariant Models: A Frequency-Domain Description of the
Limit Model 263
8.6 The Correlation Approach 269
8.7 Summary 273
8.8 Bibliography 274
8.9 Problems 275
• 9 Asymptotic Distribution of Parameter Estimates
9.1 Introduction 280
9.2 The Prediction-Error Approach: Basic Theorem 281
9.3 Expressions for the Asymptotic Variance 283
9.4 Frequency-Domain Expressions for the Asymptotic Variance 290
9.5 The Correlation Approach 296
9.6 Use and Relevance of Asymptotic Variance Expressions 302
9.7 Summary 304
9.8 Bibliography 305
9.9 Problems 305
Appendix 9A: Proof of Theorem 9.1 309
Appendix 9B: The Asymptotic Parameter Variance 313
• 10 Computing the Estimate 317
10.1 Linear Regressions and Least Squares 317
10.2 Numerical Solution by Iterative Search Methods 326
10.3 Computing Gradients 329
10.4 Two-Stage and Multistage Methods 333
10.5 Local Solutions and Initial Values 338
10.6 Subspace Methods for Estimating State Space Models 340
10.7 Summary 351
10.8 Bibliography 352
10.9 Problems 353
• 11 Recursive Estimation Methods 361
11.1 Introduction 361
11.2 The Recursive Least-Squares Algorithm 363
11.3 The Recursive IV Method 369
11.4 Recursive Prediction-Error Methods 370
11.5 Recursive Pseudolinear Regressions 374
11.6 The Choice of Updating Step 376
11.7 Implementation 382
11.8 Summary 386
11.9 Bibliography 387
11.10 Problems 388
Appendix 11 A: Techniques for Asymptotic Analysis of Recursive
Algorithms 389
11A Problems 398
• 12 Options and Objectives
12.1 Options 399
12.2 Objectives 400
12.3 Bias and Variance 404
12.4 Summary 406
12.5 Bibliography 406
12.6 Problems 406
• 13 Experiment Design 408
13.1 Some General Considerations 408
13.2 Informative Experiments 411
13.3 Input Design for Open Loop Experiments 415
13.4 Identification in Closed Loop: Identifiabilitv 428
13.5 Approaches to Closed Loop Identification 434
13.6 Optimal Experiment Design for High-Order Black-Box Models 441
13.7 Choice of Sampling Interval and Presampling Filters 444
13.8 Summary 452
13.9 Bibliography 453
13.10 Problems 454
• 14 Preprocessing Data 458
14.1 Drifts and Detrending 458
14.2 Outliers and Missing Data 461
14.3 Selecting Segments of Data and Merging Experiments 464
14.4 Prefiltering 466
14.5 Formal Design of Prefiltering and Input Properties 470
14.6 Summary 474
14.7 Bibliography 475
14.8 Problems 475
• 15 Choice of Identification Criterion 477
15.1 General Aspects 477
15.2 Choice of Norm: Robustness 479
15.3 Variance-Optimal Instruments 485
15.4 Summary 488
part iii: user's choices
15.5 Bibliography 489
15.6 Problems 490
• 16 Model Structure Selection and Model Validation 491
16.1 General Aspects of the Choice of Model Structure 491
16.2 A Priori Considerations 493
16.3 Model Structure Selection Based on Preliminary Data Analysis 495
16.4 Comparing Model Structures 498
16.5 Model Validation 509
16.6 Residual Analysis 511
16.7 Summary 516
16.8 Bibliography 517
16.9 Problems 518
• 17 System Identification in Practice 520
17.1 The Tool: Interactive Software 520
17.2 The Practical Side of System Identification 522
17.3 Some Applications 525
17.4 What Does System Identification Have To Offer? 536
• Appendix I Some Concepts From Probability Theory 539
• Appendix II Some Statistical Techniques for Linear Regressions 543
II.1 Linear Regressions and the Least Squares Estimate 543
II.2 Statistical Properties of the Least-Squares Estimate 551
II.3 Some Further Topics in Least-Squares Estimation 559
II.4 Problems 564
References 565
Subject Index 596
Reference Index 603
