System Identification Theory for the User

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ISBN: 9780136566953 | 0136566952
Cover: Hardcover
Copyright: 12/29/1998

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Appropriate for courses in System Identification. This book is a comprehensive and coherent description of the theory, methodology and practice of System Identificationthe 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 modelssuch as neural networksand methods that use frequency domain data.

Preface to the First Edition

xiv

(2)

Acknowledgments

xvi

(2)

Preface to the Second Edition

xviii

(1)

Operators and Notational Conventions

xix

1 Introduction

(17)

1.1 Dynamic Systems

(5)

1.2 Models

(2)

1.3 An Archetypical Problem--ARX Models and the Linear Least Squares Method

(5)

1.4 The System Identification Procedure

(1)

1.5 Organization of the Book

(2)

1.6 Bibliography

(2)

Part i: systems and models

(150)

2 Time-Invariant Linear Systems

(45)

2.1 Impulse Responses, Disturbances, and Transfer Functions

(10)

2.2 Frequency-Domain Expressions

(5)

2.3 Signal Spectra

(9)

2.4 Single Realization Behavior and Ergodicity Results (*)

(2)

2.5 Multivariable Systems (*)

(1)

2.6 Summary

(1)

2.7 Bibliography

(1)

2.8 Problems

(5)

Appendix 2A: Proof of Theorem 2.2

(3)

Appendix 2B: Proof of Theorem 2.3

(6)

Appendix 2C: Covariance Formulas

(2)

3 Simulation and Prediction

(16)

3.1 Simulation

(1)

3.2 Prediction

(8)

3.3 Observes

(3)

3.4 Summary

(1)

3.5 Bibliography

(1)

3.6 Problems

(3)

4 Models of Linear Time-Invariant Systems

(61)

4.1 Linear Models and Sets of Linear Models

(2)

4.2 A Family of Transfer-Function Models

(12)

4.3 State-Space Models

(10)

4.4 Distributed Parameter Models (*)

103

(2)

4.5 Model Sets, Model Structures, and Identifiability: Some Formal Aspects (*)

105

(9)

4.6 Identifiability of Some Model Structures

114

(4)

4.7 Summary

118

(1)

4.8 Bibliography

119

(2)

4.9 Problems

121

(7)

Appendix 4A: Identifiability of Black-Box Multivariable Model Structures

128

(12)

5 Models for Time-varying and Nonlinear Systems

140

(28)

5.1 Linear Time-Varying Models

140

(3)

5.2 Models with Nonlinearities

143

(3)

5.3 Nonlinear State-Space Models

146

(2)

5.4 Nonlinear Black-Box Models: Basic Principles

148

(6)

5.5 Nonlinear Black-Box Models: Neural Networks, Wavelets and Classical Models

154

(2)

5.6 Fuzzy Models

156

(5)

5.7 Formal Characterization of Models (*)

161

(3)

5.8 Summary

164

(1)

5.9 Bibliography

165

(1)

5.10 Problems

165

(3)

Part ii: methods

168

(231)

6 Nonparametric Time-and Frequency-Domain Methods

168

(29)

6.1 Transient-Response Analysis and Correlation Analysis

168

(2)

6.2 Frequency-Response Analysis

170

(3)

6.3 Fourier Analysis

173

(5)

6.4 Spectral Analysis

178

(9)

6.5 Estimating the Disturbance Spectrum (*)

187

(2)

6.6 Summary

189

(1)

6.7 Bibliography

190

(1)

6.8 Problems

191

(3)

Appendix 6A: Derivation of the Asymptotic Properties of the Spectral Analysis Estimate

194

(3)

7 Parameter Estimation Methods

197

(50)

7.1 Guiding Principles Behind Parameter Estimation Methods

197

(2)

7.2 Minimizing Prediction Errors

199

(4)

7.3 Linear Regressions and the Least-Squares Method

203

(9)

7.4 A Statistical Framework for Parameter Estimation and the Maximum Likelihood Method

212

(10)

7.5 Correlating Prediction Errors with Past Data

222

(2)

7.6 Instrumental-Variable Methods

224

(3)

7.7 Using Frequency Domain Data to Fit Linear Models (*)

227

(6)

7.8 Summary

233

(1)

7.9 Bibliography

234

(2)

7.10 Problems

236

(9)

Appendix 7A: Proof of the Cramer-Rao Inequality

245

(2)

8 Convergence and Consistency

247

(33)

8.1 Introduction

247

(2)

8.2 Conditions on the Data Set

249

(4)

8.3 Prediction-Error Approach

253

(5)

8.4 Consistency and Identifiability

258

(5)

8.5 Linear Time-Invariant Models: A Frequency-Domain Description of the Limit Model

263

(6)

8.6 The Correlation Approach

269

(4)

8.7 Summary

273

(1)

8.8 Bibliography

274

(1)

8.9 Problems

275

(5)

9 Asymptotic Distribution of Parameter Estimates

280

(37)

9.1 Introduction

280

(1)

9.2 The Prediction-Error Approach: Basic Theorem

281

(2)

9.3 Expressions for the Asymptotic Variance

283

(7)

9.4 Frequency-Domain Expressions for the Asymptotic Variance

290

(6)

9.5 The Correlation Approach

296

(6)

9.6 Use and Relevance of Asymptotic Variance Expressions

302

(2)

9.7 Summary

304

(1)

9.8 Bibliography

305

(1)

9.9 Problems

305

(4)

Appendix 9A: Proof of Theorem 9.1

309

(4)

Appendix 9B: The Asymptotic Parameter Variance

313

(4)

10 Computing the Estimate

317

(44)

10.1 Linear Regressions and Least Squares

317

(9)

10.2 Numerical Solution by Iterative Search Methods

326

(3)

10.3 Computing Gradients

329

(4)

10.4 Two-Stage and Multistage Methods

333

(5)

10.5 Local Solutions and Initial Values

338

(2)

10.6 Subspace Methods for Estimating State Space Models

340

(11)

10.7 Summary

351

(1)

10.8 Bibliography

352

(1)

10.9 Problems

353

(8)

11 Recursive Estimation Methods

361

(38)

11.1 Introduction

361

(2)

11.2 The Recursive Least-Squares Algorithm

363

(6)

11.3 The Recursive IV Method

369

(1)

11.4 Recursive Prediction-Error Methods

370

(4)

11.5 Recursive Pseudolinear Regressions

374

(2)

11.6 The Choice of Updating Step

376

(6)

11.7 Implementation

382

(4)

11.8 Summary

386

(1)

11.9 Bibliography

387

(1)

11.10 Problems

388

(1)

Appendix 11A: Techniques for Asymptotic Analysis of Recursive Algorithms

389

(9)

11A Problems

398

(1)

part iii: user's choices

399

(166)

12 Options and Objectives

399

(9)

12.1 Options

399

(1)

12.2 Objectives

400

(4)

12.3 Bias and Variance

404

(2)

12.4 Summary

406

(1)

12.5 Bibliography

406

(1)

12.6 Problems

406

(2)

13 Experiment Design

408

(50)

13.1 Some General Considerations

408

(3)

13.2 Informative Experiments

411

(4)

13.3 Input Design for Open Loop Experiments

415

(13)

13.4 Identification in Closed Loop: Identifiability

428

(6)

13.5 Approaches to Closed Loop Identification

434

(7)

13.6 Optimal Experiment Design for High-Order Black-Box Models

441

(3)

13.7 Choice of Sampling Interval and Presampling Filters

444

(8)

13.8 Summary

452

(1)

13.9 Bibliography

453

(1)

13.10 Problems

454

(4)

14 Preprocessing Data

458

(19)

14.1 Drifts and Detrending

458

(3)

14.2 Outliers and Missing Data

461

(3)

14.3 Selecting Segments of Data and Merging Experiments

464

(2)

14.4 Prefiltering

466

(4)

14.5 Formal Design of Prefiltering and Input Properties

470

(4)

14.6 Summary

474

(1)

14.7 Bibliography

475

(1)

14.8 Problems

475

(2)

15 Choice of Identification Criterion

477

(14)

15.1 General Aspects

477

(2)

15.2 Choice of Norm: Robustness

479

(6)

15.3 Variance-Optimal Instruments

485

(3)

15.4 Summary

488

(1)

15.5 Bibliography

489

(1)

15.6 Problems

490

(1)

16 Model Structure Selection and Model Validation

491

(29)

16.1 General Aspects of the Choice of Model Structure

491

(2)

16.2 A Priori Considerations

493

(2)

16.3 Model Structure Selection Based on Preliminary Data Analysis

495

(3)

16.4 Comparing Model Structures

498

(11)

16.5 Model Validation

509

(2)

16.6 Residual Analysis

511

(5)

16.7 Summary

516

(11)

16.8 Bibliography

517

(1)

16.9 Problems

518

(2)

17 System Identification in Practice

520

(19)

17.1 The Tool: Interactive Software

520

(2)

17.2 The Practical Side of System Identification

522

(3)

17.3 Some Applications

525

(11)

17.4 What Does System Identification Have To Offer?

536

(3)

Appendix I Some Concepts From Probability Theory

539

(4)

Appendix II Some Statistical Techniques for Linear Regressions

543

(22)

II.1 Linear Regressions and the Least Squares Estimate

543

(8)

II.2 Statistical Properties of the Least-Squares Estimate

551

(8)

II.3 Some Further Topics in Least-Squares Estimation

559

(6)

II.4 Problems

564

(1)

References

565

(31)

Subject Index

596

(7)

Reference Index

603

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System Identification Theory for the User

Summary

Author Biography

Table of Contents

Supplemental Materials