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The cost of complexity in system identification: The Output Error case
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0003-0355-2663
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)
The University of Newcastle, Australia.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0002-9368-3079
2011 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 47, no 9, 1938-1948 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we investigate the cost of complexity, which is defined as the minimum amount of input power required to estimate the frequency response of a given linear time invariant system of order n with a prescribed degree of accuracy. In particular we require that the asymptotic (in the data length) variance is less or equal to gamma over a prespecified frequency range [0, omega(B)]. The models considered here are Output Error models, with an emphasis on fixed denominator and Laguerre models. Several properties of the cost are derived. For instance, we present an expression which shows how the pole of the Laguerre model affects the cost. These results quantify how the cost of the system identification experiment depends on n and on the model structure. Also, they show the relation between the cost and the amount of information we would like to extract from the system (in terms of omega(B) and gamma). For simplicity we assume that there is no undermodelling.

Place, publisher, year, edition, pages
2011. Vol. 47, no 9, 1938-1948 p.
Keyword [en]
Experiment design, System identification, Prediction error method, LMI optimization, Asymptotic variance
National Category
Control Engineering
Research subject
SRA - ICT
Identifiers
URN: urn:nbn:se:kth:diva-41792DOI: 10.1016/j.automatica.2011.06.021ISI: 000294877400010Scopus ID: 2-s2.0-80052032229OAI: oai:DiVA.org:kth-41792DiVA: diva2:445242
Funder
Swedish Research Council, 621-2007-6271Swedish Research Council, 621-2009-4017
Note

QC 20150723

Available from: 2011-10-03 Created: 2011-10-03 Last updated: 2017-12-08Bibliographically approved

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Rojas, Cristian R.Hjalmarsson, Håkan

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