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Nonlinear black-box modeling in system identification: A unified overview
Department of Electrical Engineering, Linköping University. (Reglerteknik, Automatic Control)
Department of Electrical Engineering, Linköping University. (Reglerteknik, Automatic Control)
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1995 (English)In: Automatica, ISSN 00051098 (ISSN), Vol. 31, no 12, 1691-1724 p.Article in journal (Refereed) Published
Abstract [en]

A nonlinear black-box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area, with structures based on neural networks, radial basis networks, wavelet networks and hinging hyperplanes, as well as wavelet-transform-based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function expansion. The basis functions are typically formed from one simple scalar function, which is modified in terms of scale and location. The expansion from the scalar argument to the regressor space is achieved by a radial- or a ridge-type approach. Basic techniques for estimating the parameters in the structures are criterion minimization, as well as two-step procedures, where first the relevant basis functions are determined, using data, and then a linear least-squares step to determine the coordinates of the function approximation. A particular problem is to deal with the large number of potentially necessary parameters. This is handled by making the number of 'used' parameters considerably less than the number of 'offered' parameters, by regularization, shrinking, pruning or regressor selection. Copyright © 1995 Elsevier Science Ltd All rights reserved.

Place, publisher, year, edition, pages
1995. Vol. 31, no 12, 1691-1724 p.
Keyword [en]
Fuzzy modeling, Model structures, Neural networks, Nonlinear systems, Parameter estimation, Wavelets, Computer simulation, Conformal mapping, Fuzzy sets, Least squares approximations, Mathematical models, Regression analysis, Vectors, Wavelet transforms, Basis function expansion, Hinging hyperplanes, Nonlinear black box modeling, Nonlinear mapping, Radial basis networks, Regression vector, Wavelet networks, Identification (control systems)
National Category
Control Engineering
Research subject
URN: urn:nbn:se:kth:diva-60589DOI: 10.1016/0005-1098(95)00120-8OAI: diva2:477544
NR 20140805Available from: 2012-01-13 Created: 2012-01-13 Last updated: 2012-01-13Bibliographically approved

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Hjalmarsson, Håkan
Control Engineering

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