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More About This Title Model Identification and Data Analysis
English
This book is about constructing models from experimental data. It covers a range of topics, from statistical data prediction to Kalman filtering, from black-box model identification to parameter estimation, from spectral analysis to predictive control.
Written for graduate students, this textbook offers an approach that has proven successful throughout the many years during which its author has taught these topics at his University.
The book:
- Contains accessible methods explained step-by-step in simple terms
- Offers an essential tool useful in a variety of fields, especially engineering, statistics, and mathematics
- Includes an overview on random variables and stationary processes, as well as an introduction to discrete time models and matrix analysis
- Incorporates historical commentaries to put into perspective the developments that have brought the discipline to its current state
- Provides many examples and solved problems to complement the presentation and facilitate comprehension of the techniques presented
English
SERGIO BITTANTI is Emeritus Professor of Model Identification and Data Analysis (MIDA) at the Politecnico di Milano, Milan, Italy, where his intense activity of research and teaching has attracted the attention of many young researchers.
He started teaching the course of MIDA years ago, with just a few students. Today the course is offered in various sections with about one thousand students.
He has organized a number of workshops and conferences, and has served as member of the Program Committee of more than 70 international congresses.
He has for many years been associated with the National Research Council (CNR) of Italy and is a member of the Academy of Science and Literature of Milan (Istituto Lombardo – Accademia di Scienze e Lettere).
He received many awards, in particular the title of Ambassador of the city of Milan and the medal of the President of the Italian Republic for the IFAC World Congress held in Milan in 2011 with a record number of attendees from 73 Countries.
Website: http://home.deib.polimi.it/bittanti/
English
Introduction vii
1 Stationary Processes and Time Series 1
1.1 Introduction 1
1.2 The prediction problem 2
1.3 Random variable 5
1.4 Random vector 6
1.5 Stationary process 9
1.6 White process 12
1.7 MA process 12
1.8 AR process 17
1.9 Yule-Walker equations 21
1.10 ARMA process 24
1.11 Spectrum of a stationary process 25
1.12 ARMA model: stability test and variance computation 27
1.13 Fundamental theorem of spectral analysis 36
1.14 Spectrum drawing 39
1.15 Proof of the fundamental theorem of spectral analysis 45
1.16 Representations of a stationary process 48
2 Estimation of Process Characteristics 49
2.1 Introduction 49
2.2 General properties of the covariance function 49
2.3 Covariance function of ARMA processes 51
2.4 Estimation of the mean 53
2.5 Estimation of the covariance function 56
2.6 Estimation of the spectrum 57
2.7 Whiteness test 60
3 Prediction 63
3.1 Introduction 63
3.2 Fake predictor 64
3.3 Spectral factorization 68
3.4 Whitening filter 73
3.5 Optimal predictor from data 74
3.6 Prediction of an ARMA process 78
3.7 ARMAX process 81
3.8 Prediction of an ARMAX process 82
4 Model Identification 85
4.1 Introduction 85
4.2 Setting the identification problem 87
4.3 Static modelling 89
4.4 Dynamic modelling 96
4.5 External representation models 96
4.6 Internal representation models 101
4.7 The model identification process 105
4.8 The predictive approach 106
4.9 Models in predictive form 108
5 Identification of Input-Output Models 111
5.1 Introduction 111
5.2 Estimating AR and ARX models: the Least Squares method 111
5.3 Identifiability 114
5.4 Estimating ARMA and ARMAX models 119
5.5 Asymptotic analysis 129
5.6 Recursive identification 144
5.7 Robustness of identification methods 153
5.8 Parameter tracking 156
6 Model Complexity Selection 163
6.1 Introduction 163
6.2 Cross-validation 165
6.3 FPE criterion 166
6.4 AIC criterion 169
6.5 MDL criterion 170
6.6 Durbin-Levinson algorithm 173
7 Identification of State-Space Models 181
7.1 Introduction 181
7.2 Hankel matrix 183
7.3 Order determination 184
7.4 Determination of matrices G and H 185
7.5 Determination of matrix F 186
7.6 Mid summary: an ideal procedure 187
7.7 Order determination with SVD 187
7.8 Reliable identification of a state-space model 189
8 Predictive Control 195
8.1 Introduction 195
8.2 Minimum Variance control 196
8.3 Generalized Minimum Variance control 205
8.4 Model based predictive control 213
8.5 Data driven control synthesis 215
9 Kalman Filtering and Prediction 219
9.1 Introduction 219
9.2 Kalman approach to prediction and filtering problems 221
9.3 The Bayes estimation problem 223
9.4 One-step-ahead Kalman predictor 235
9.5 Multi-step optimal predictor 249
9.6 Optimal filter 251
9.7 Steady-state predictor 253
9.8 Innovation representation 280
9.9 Innovation representation versus canonical representation 280
9.10 K-theory versus K-W theory 281
9.11 Extended Kalman filter - EKF 286
9.12 The robust approach to filtering 288
10 Parameter Identification in a Given Model 297
10.1 Introduction 297
10.2 Kalman filter based approaches 298
10.3 Two Stage method 301
11 Case Studies 307
11.1 Introduction 307
11.2 Kobe earthquake data analysis 307
11.3 Estimation of a sinusoid in noise 315
Appendix A - Linear Dynamical Systems 327
A.1 State-space and input-output models 327
A.2 Lagrange formula 330
A.3 Stability 331
A.4 Impulse response 332
A.5 Frequency response 334
A.6 Multiplicity of state-space models 334
A.7 Reachability and observability 337
A.8 System decomposition 342
A.9 Stabilizability and detectability 347
Appendix B - Matrices 349
B.1 Basics 349
B.2 Eigenvalues 354
B.3 Determinant and inverse 355
B.4 Rank 359
B.5 Annihilating polynomial 361
B.6 Algebraic and geometric multiplicity 364
B.7 Range and null space 365
B.8 Quadratic forms 366
B.9 Derivative of a scalar function with respect to a vector 369
B.10 Matrix diagonalization via similarity 369
B.11 Matrix diagonalization via Singular Value Decomposition 370
B.12 Matrix norm and condition number 373
Appendix C - Problems And Solutions 377
Bibliography 411
