9780136566953

System Identification Theory for the User

by
  • ISBN13:

    9780136566953

  • ISBN10:

    0136566952

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 1998-12-29
  • Publisher: Prentice Hall

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Summary

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.

Author Biography

LENNART LJUNG is Professor of the Chair of Automatic Control in the Department of Electrical Engineering, Linkšping University, Sweden. He is the author of nine books and over 100 articles in refereed international journals, as well as the author of the field's leading software package, System Identification Toolbox for MATLAB.

Table of Contents

Preface to the First Edition xiv(2)
Acknowledgments xvi(2)
Preface to the Second Edition xviii(1)
Operators and Notational Conventions xix
1 Introduction
1(17)
1.1 Dynamic Systems
1(5)
1.2 Models
6(2)
1.3 An Archetypical Problem--ARX Models and the Linear Least Squares Method
8(5)
1.4 The System Identification Procedure
13(1)
1.5 Organization of the Book
14(2)
1.6 Bibliography
16(2)
Part i: systems and models 18(150)
2 Time-Invariant Linear Systems
18(45)
2.1 Impulse Responses, Disturbances, and Transfer Functions
18(10)
2.2 Frequency-Domain Expressions
28(5)
2.3 Signal Spectra
33(9)
2.4 Single Realization Behavior and Ergodicity Results (*)
42(2)
2.5 Multivariable Systems (*)
44(1)
2.6 Summary
45(1)
2.7 Bibliography
46(1)
2.8 Problems
47(5)
Appendix 2A: Proof of Theorem 2.2
52(3)
Appendix 2B: Proof of Theorem 2.3
55(6)
Appendix 2C: Covariance Formulas
61(2)
3 Simulation and Prediction
63(16)
3.1 Simulation
63(1)
3.2 Prediction
64(8)
3.3 Observes
72(3)
3.4 Summary
75(1)
3.5 Bibliography
75(1)
3.6 Problems
76(3)
4 Models of Linear Time-Invariant Systems
79(61)
4.1 Linear Models and Sets of Linear Models
79(2)
4.2 A Family of Transfer-Function Models
81(12)
4.3 State-Space Models
93(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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