Nonparametric System Identification

by Wlodzimierz Greblicki , Miroslaw Pawlak

ISBN13: 9780521868044

ISBN10: 0521868041

Format: Hardcover

Pub. Date: 2008-06-16

Publisher(s): Cambridge University Press

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Summary

Presenting a thorough overview of the theoretical foundations of non-parametric system identification for nonlinear block-oriented systems, this books shows that non-parametric regression can be successfully applied to system identification, and it highlights the achievements in doing so. With emphasis on Hammerstein, Wiener systems, and their multidimensional extensions, the authors show how to identify nonlinear subsystems and their characteristics when limited information exists. Algorithms using trigonometric, Legendre, Laguerre, and Hermite series are investigated, and the kernel algorithm, its semirecursive versions, and fully recursive modifications are covered. The theories of modern non-parametric regression, approximation, and orthogonal expansions, along with new approaches to system identification (including semiparametric identification), are provided. Detailed information about all tools used is provided in the appendices. This book is for researchers and practitioners in systems theory, signal processing, and communications and will appeal to researchers in fields like mechanics, economics, and biology, where experimental data are used to obtain models of systems.

Author Biography

Miroslaw Pawlak is a professor in the Department of Electrical and Computer Engineering at the University of Manitoba, Canada.

Preface	p. ix
Introduction	p. 1
Discrete-time Hammerstein systems	p. 3
The system	p. 3
Nonlinear subsystem	p. 4
Dynamic subsystem identification	p. 8
Bibliographic notes	p. 9
Kernel algorithms	p. 11
Motivation	p. 11
Consistency	p. 13
Applicable kernels	p. 14
Convergence rate	p. 16
The mean-squared error	p. 21
Simulation example	p. 21
Lemmas and proofs	p. 24
Bibliographic notes	p. 29
Semirecursive kernel algorithms
Introduction	p. 30
Consistency and convergence rate	p. 31
Simulation example	p. 34
Proofs and lemmas	p. 35
Bibliographic notes	p. 43
Recursive kernel algorithms	p. 44
Introduction	p. 44
Relation to stochastic approximation	p. 44
Consistency and convergence rate	p. 46
Simulation example	p. 49
Auxiliary results, lemmas, and proofs	p. 51
Bibliographic notes	p. 58
Orthogonal series algorithms	p. 59
Introduction	p. 59
Fourier series estimate	p. 61
Legendre series estimate	p. 64
Laguerre series estimate	p. 66
Hermite series estimate	p. 68
Wavelet estimate	p. 69
Local and global errors	p. 70
Simulation example	p. 71
Lemmas and proofs	p. 72
Bibliographic notes	p. 78
Algorithms with ordered observations	p. 80
Introduction	p. 80
Kernel estimates	p. 81
Orthogonal series estimates	p. 85
Lemmas and proofs	p. 89
Bibliographic notes	p. 99
Continuous-time Hammerstein systems	p. 101
Identification problem	p. 101
Kernel algorithm	p. 103
Orthogonal series algorithms	p. 106
Lemmas and proofs	p. 108
Bibliographic notes	p. 112
Discrete-time Wiener systems	p. 113
The system	p. 113
Nonlinear subsystem	p. 114
Dynamic subsystem identification	p. 119
Lemmas	p. 121
Bibliographic notes	p. 122
Kernel and orthogonal series algorithms	p. 123
Kernel algorithms	p. 123
Orthogonal series algorithms	p. 126
Simulation example	p. 129
Lemmas and proofs	p. 130
Bibliographic notes	p. 142
Continuous-time Wiener system	p. 143
Identification problem	p. 143
Nonlinear subsystem	p. 144
Dynamic subsystem	p. 146
Lemmas	p. 146
Bibliographic notes	p. 148
Other block-oriented nonlinear systems	p. 149
Series-parallel, block-oriented systems	p. 149
Block-oriented systems with nonlinear dynamics	p. 173
Concluding remarks	p. 218
Bibliographical notes	p. 220
Multivariate nonlinear block-oriented systems	p. 222
Multivariate nonparametric regression	p. 222
Additive modeling and regression analysis	p. 228
Multivariate systems	p. 242
Concluding remarks	p. 248
Bibliographic notes	p. 248
Semiparametric identification	p. 250
Introduction	p. 250
Semiparametric models	p. 252
Statistical inference for semiparametric models	p. 255
Statistical inference for semiparametric Wiener models	p. 264
Statistical inference for semiparametric Hammerstein models	p. 286
Statistical inference for semiparametric parallel models	p. 287
Direct estimators for semiparametric systems	p. 290
Concluding remarks	p. 309
Auxiliary results, lemmas, and proofs	p. 310
Bibliographical notes	p. 316
Convolution and kernel functions	p. 319
Introduction	p. 319
Convergence	p. 320
Applications to probability	p. 328
Lemmas	p. 329
Orthogonal functions	p. 331
Introduction	p. 331
Fourier series	p. 333
Legendre series	p. 340
Laguerre series	p. 345
Hermite series	p. 351
Wavelets	p. 355
Probability and statistics	p. 359
White noise	p. 359
Convergence of random variables	p. 361
Stochastic approximation	p. 364
Order statistics	p. 365
References	p. 371
Index	p. 387
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