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Nonlinear black-box models in system identification: Mathematical foundations
Department of Electrical Engineering, Linköping University. (Reglerteknik, Automatic Control)ORCID iD: 0000-0002-9368-3079
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1995 (English)In: Automatica, ISSN 00051098 (ISSN), Vol. 31, no 12, 1725-1750 p.Article in journal (Refereed) Published
Abstract [en]

We discuss several aspects of the mathematical foundations of the nonlinear black-box identification problem. We shall see that the quality of the identification procedure is always a result of a certain trade-off between the expressive power of the model we try to identify (the larger the number of parameters used to describe the model, the more flexible is the approximation), and the stochastic error (which is proportional to the number of parameters). A consequence of this trade-off is the simple fact that a good approximation technique can be the basis of a good identification algorithm. From this point of view, we consider different approximation methods, and pay special attention to spatially adaptive approximants. We introduce wavelet and 'neuron' approximations, and show that they are spatially adaptive. Then we apply the acquired approximation experience to estimation problems. Finally, we consider some implications of these theoretical developments for the practically implemented versions of the 'spatially adaptive' algorithms. Copyright © 1995 Elsevier Science Ltd All rights reserved.

Place, publisher, year, edition, pages
1995. Vol. 31, no 12, 1725-1750 p.
Keyword [en]
Neural networks, Non-parametric identification, Nonlinear systems, Wavelet estimators, Algorithms, Approximation theory, Computer simulation, Errors, Mathematical models, Parameter estimation, Random processes, Regression analysis, Wavelet transforms, Mathematical foundations, Nonlinear black box models, Spatially adaptive approximant, Stochastic error, Wavelet estimator, Identification (control systems)
National Category
Control Engineering
Research subject
URN: urn:nbn:se:kth:diva-60588DOI: 10.1016/0005-1098(95)00119-1OAI: diva2:477566
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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