System Identification Theory for the User

by Ljung, Lennart

• ISBN13: 9780136566953
• ISBN10: 0136566952
• Edition: 2nd
• Format: Hardcover
• Copyright: 1998-12-29
• Publisher: PEARSO

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