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On the choice of norms in system identification
Department of Electrical Engineering, Linköping University. (Reglerteknik, Automatic Control)ORCID iD: 0000-0002-9368-3079
Department of Electrical Engineering, Linköping University. (Reglerteknik, Automatic Control)
1996 (English)In: IEEE Transactions on Automatic Control, ISSN 00189286 (ISSN), Vol. 41, no 9, 1367-1372 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all ℓp-norms, p ≀ 2 < ∞ for F(C). ©1996 IEEE.

Place, publisher, year, edition, pages
1996. Vol. 41, no 9, 1367-1372 p.
Keyword [en]
Convergence of numerical methods, Mathematical models, Robustness (control systems), Statistical methods, Parameter estimate variance, Prediction error system, Identification (control systems)
National Category
Control Engineering
Research subject
URN: urn:nbn:se:kth:diva-60585DOI: 10.1109/9.536512OAI: diva2:477547
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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