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The Cost of Complexity in System Identification: Frequency Function Estimation of Finite Impulse Response Systems
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.
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
2010 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, no 10, 2298-2309 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider full order modeling, i.e., when the true system belongs to the model set. We investigate the minimum amount of input energy required to estimate a given linear system with a full order model within a prescribed degree of accuracy gamma, as a function of the model complexity. This quantity we define to be the "cost of complexity." The degree of accuracy is measured by the inverse of the maximum variance of the discrete-time frequency function estimator over a given frequency range [-omega(B), omega(B)]. It is commonly believed that the cost increases as the model complexity increases. However, the amount of information that is to be extracted from the system also influences the cost. The objective of this paper is to quantify these dependencies for systems described by finite-impulse response models. It is shown that, asymptotically in the model order and sample size, the cost is well approximated by gamma sigma(2)(o)n omega(B)/pi where sigma(2)(o)is the noise variance. This expression can be used as a simple rule of thumb for assessing trade-offs that have to be made in a system identification project where full order models are used. For example, for given experiment duration, excitation level and desired accuracy, one can assess how the achievable frequency range depends on the required model order. This type of consideration is useful when formally planning experiments. In addition, we establish several properties of the cost of complexity. We find, for example, that if omega(B) is very close (but not necessarily equal) to pi, the optimal input satisfies the model quality constraint for all frequencies.

Place, publisher, year, edition, pages
2010. Vol. 55, no 10, 2298-2309 p.
Keyword [en]
Asymptotic, finite-impulse response (FIR), linear matrix inequalities (LMIs)
National Category
Control Engineering
Research subject
SRA - ICT
Identifiers
URN: urn:nbn:se:kth:diva-26272DOI: 10.1109/TAC.2010.2063470ISI: 000283362600007Scopus ID: 2-s2.0-77957706931OAI: oai:DiVA.org:kth-26272DiVA: diva2:387584
Funder
Swedish Research Council, 621-2007-6271
Note

QC 20110114

Available from: 2011-01-14 Created: 2010-11-21 Last updated: 2017-12-11Bibliographically approved

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Rojas, Cristian R.Hjalmarsson, Håkan

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