Nonparametric System Identification

Abstract

Presenting a thorough overview of the theoretical foundations of non-parametric system identification for nonlinear block-oriented systems, this book 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.

On-line wavelet estimation of Hammerstein system nonlinearity

“…Therefore, the algorithm replicates the asymptotic behavior of the aforementioned on-line nonparametric algorithms (and hence possesses the same limit properties as their off-line prototypes, cf. the results of Greblicki and Pawlak (2008), Hasiewicz et al (2005)), offering additionally-practically important-advantages (collected in Table 1), cf. the works of ) andŚliwiński et al (2007.…”

“…The algorithm, in the wavelet version, is of the following form (Greblicki, 2002;Greblicki and Pawlak, 2008, Chapter 5):…”

“…Nevertheless, there is a class of distribution-free quotient algorithms (including, in particular, those based on the rectangular kernel or on the Haar series kernel), whose asymptotic behavior is not affected by the smoothness of the density function Györfi et al (2002, Chapter 4.1), Greblicki and Pawlak (2008, Chapter 3), Rutkowski (2004). Furthermore, algorithms based on order statistics possess densityindependent asymptotic properties; (Śliwiński and Hasiewicz, 2009;Śliwiński et al, 2009;Greblicki and Pawlak, 2008, Chapter 7), however, they need all the measurements to be stored during identification.…”

MINLIP for the identification of monotone Wiener systems

“…Different existing approaches could roughly be divided in methods using (i) Invertible nonlinearities (reducing to Hammerstein identification), (ii) correlation based approaches exploiting stochastic properties of the signals [3,1], (iii) approximate (recursive) PEM approaches providing a wellestablished framework for convergence analysis [16,17] and [6], (iv) subspace based approaches [15]. For a general overview see the survey [5]. Specific applications towards identification with quantized outputs are considered in [18], see also the book [12].…”

An efficient stochastic approximation EM algorithm using conditional particle filters

“…See e.g. [57,17,35,19,39,18,24,51] and the references therein. However, the approach presented here differs from the existing literature on several accounts.…”