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(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

(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

3．1 Simulation 63

(3 Simulation and Predition 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 Identifiability: Some Formal Aspects（*） 105

4．6 Identifiability of Some Model Structures 114

4．7 Summary 118

4．8 Bibliography 119

4．9 Problems 121

Appendix 4A: Identifiability 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

(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 Cramér-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 Identifiability 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 280

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 11A: Techniques for Asymptotic Analysis of Recursive Algorithms 389

11A Problems 398

(12 Options and Objectives 399

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:Identifiability 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

14．8 Problems 475

14．7 Bibliography 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

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

(AppendixⅠSome Concepts From Probability Theory 539

( AppendixⅡ 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