Prebce to the First Edition Acknowledgments Preface to the Second Edition Operators and Notational Conventions 1 Introduction 1.1 Dynamic Systems 1.2 Models 1.3 An Archetypical Problem----ARX Models and the Linear Least Squares Method 1.4 The System Identification Procedure 1.5 Organization of the Book 1.6 Bibliography
part i: systems and models 2 Time-Invariant Linear Systems 2.1 Impulse Responses, Disturbances, and Transfer Functions 2.2 Frequency-Domain Expressions 2.3 Signal Spectra 2.4 Single Realisation Behavior and Ergodicity Results (*) 2.5 Multivariable Systems (*) 2.6 Sununary 2.7 Biblingraphy 2.8 Problems Appendis 2A: Proof of Theorem 2.2 Appendis 2B: Proof of Theorem 2.3 Appendis 2C: Covariance Formulas
4 Models of Linear Time-Invariant Systems 4.1 Linear Models and Sets of Linear Models 4.2 A Family of Transfer-Function Models 4.3 State-Space Models 4.4 Distributed Parameter Models (*) 4.5 Model Sets, Model Structures, and Identifiability: Some Formal Aspects(*) 4.6 Identifiability of Some Model Structures 4.7 Summary 4.8 Bibliography 4.9 Problems Appendix 4A: Identifiability of Black-Box Multivariable Model Structures
5 Models for Time-varying and Nonlinear Systems 5.1 Linear Time-Varying Models 5.2 Models with Nonlinearities 5.3 Nonlinear State-Space Models 5.4 Nonlinear Black-Box Models: Basic Principles 5.5 Nonlinear Black-Box Models: Neural Networks, Wavelets and Classical Models 5.6 Fuzzy Models 5.7 Formal Characterization of Models (*) 5.8 Summary 5.9 Bibliography 5.10 Problems
part ii:methods 6 Nonparametric Time- and Frequency-Domain Methods 6.1 Transient-Response Analysis and Correlation Analysis 6.2 Frequency-Response Analysis 6.3 Fourier Analysis 6.4 Spectral Analysis 6.5 Estimating the Disturbance Spectrum (*) 6.6 Summary 6.7 Bibliography 6.8 Problems Appendix 6A: Derivation of the AsymPtotic Properties of the Spectral Analysis Estimate
7 Parameter Estimation Methods 7.1 Guiding Principles Behind Parameter Estimation Methods 7.2 Minimising Prediction Errors 7.3 Linear Regressions and the Least-Squares Method 7.4 A Statistical Framework for Parameter Estimation and the Maximum Likelihood Method 7.5 Correlating Prediction Errors with Past Data 7.6 Instrumentatwriable Methods 7.7 Using Frequency Domain Data to Fit Linear Models (*) 7.8 Summary 7.9 Bibliography 7.10 Problems Appendix 7A: Proof of the Cramer-Rao Inequality
8 Convergence and Consistency 8.1 Introduction 8.2 Conditions on the Data Set 8.3 Prediction-Error Approach 8.4 Consistency and Identifiability 8.5 Linear Time-Invariant Models: A Frequency-Domain Description of the Limit Model 8.6 The Correlation Approach 8.7 Summary 8.8 Bibliography 8.9 Problems
9 Asymptotic Distribution of Parameter Estimates 9.1 Introduction 9.2 The Prediction-Error Approach: Basic Theorem 9.3 Expressions for the Asymptotic Variance 9.4 Frequency-Domain Expressions for the Asymptotic Variance 9.5 The Correlation Approach 9.6 Use and Relevance of Asymptotic Variance Expressions 9.7 Summary 9.8 Bibliography 9.9 Problems Appendix 9A: Proof of Theorem 9.1 Appendix 9B: The Asymptotic Parameter Variance
10 Computing the Estimate 10.1 Linear Regressions and beast Squares 10.2 Numerical Solution by Iterative Search Methods 10.3 Computing Gradients 10.4 Two-Stage and Multistage Methods 10.5 Local Solutions and Initial Values 10.6 Subspace Methods for Estimating State Space Models 10.7 Summary 10.8 Bibliography 10.9 Problems
11 Recursive Estimation Methods 11.1 Introduction 11.2 The Recursive Least-Squares Algorithm 11.3 The Recursive IV Method 1l.4 Recursive Prediction-Error Methods 11.5 Recursive Pseudolinear Regressions 11.6 The Choice of Updating Step 11.7 Implementation 11.8 Summary 11.9 Bibliography 11.10 Problems Appendix 11A: Techniques for Asymptotic Analysis of Recursive Algorithms 11A Problems
part iii: user's choices 12 Options and Objectives 12.1 Options 12.2 Objectives 12.3 Bias and Variance 12.4 Summary 12.5 Bibliography 12.6 Problems
13 Experiment Design 13.1 Some General Considerations 13.2 Informative Experiments 13.3 Input Design for Open Loop Experiments 13.4 Identification in Closed Loop: Identifiability 13.5 Approaches to Closed Loop Identification 13.6 Optimal Experiment Design for High-Order Black-Box Models 13.7 Choice of Sampling Interval and Presampling Filters 13.8 Summary 13.9 Bibliography 13.10 Problems
14 Preprocessing Data 14.1 Drifts and Detrending 14.2 Outliers and Missing Data 14.3 Selecting Segments of Data and Merging Experiments 14.4 Prefiltering 14.5 Formal Design of Prefiltering and Input Properties 14.6 Summary 14.7 Bibliography 14.8 Problems
15 Choice of Identification Criterion 15.1 General Aspects 15.2 Choice of Norm: Robustness 15.3 Variance-Optimal Instruments 15.4 Summary 15.5 Bibliography l5.6 Problems
16 Model Structure Selection and Model Validation 16.1 General Aspects of the Choice of Model Structure 16.2 A Priori Considerations 16.3 Model Structure Selection Based on Preliminary Data Analysis 16.4 Comparing Model Structures 16.5 Model Validation 16.6 Residual Analysis 16.7 Summary 16.8 Bibliography 16.9 Problems
17 System Identification in Practice 17.1 The Tool: Interactive Software 17.2 The Practical Side of System Identification 17.3 Some Applications 17.4 What Does System Identification Have To Offer? Appendix I Some Concepts From Probability Theory Appendix II Some Statistical Techniques for Linear Regressions II.1 Linear Regressions and the Least Squares Estimate II.2 Statistical Properties of the Least-Squares Estimate II.3 Some Further Topics in Least-Squares Estimation II.4 Problems
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