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Parametric Identification Using Weighted Null-Space Fitting
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0003-0355-2663
KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.ORCID iD: 0000-0002-9368-3079
2019 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 64, no 7, p. 2798-2813Article in journal (Refereed) Published
Abstract [en]

In identification of dynamical systems, the prediction error method with a quadratic cost function provides asymptotically efficient estimates under Gaussian noise, but in general it requires solving a nonconvex optimization problem, which may imply convergence to nonglobal minima. An alternative class of methods uses a nonparametric model as intermediate step to obtain the model of interest. Weighted null-space fitting (WNSF) belongs to this class, starting with the estimate of a nonparametric ARX model with least squares. Then, the reduction to a parametric model is a multistep procedure where each step consists of the solution of a quadratic optimization problem, which can be obtained with weighted least squares. The method is suitable for both open- and closed-loop data, and can be applied to many common parametric model structures, including output-error, ARMAX, and Box-Jenkins. The price to pay is the increase of dimensionality in the nonparametric model, which needs to tend to infinity as function of the sample size for certain asymptotic statistical properties to hold. In this paper, we conduct a rigorous analysis of these properties: namely, consistency, and asymptotic efficiency. Also, we perform a simulation study illustrating the performance of WNSF and identify scenarios where it can be particularly advantageous compared with state-of-the-art methods.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2019. Vol. 64, no 7, p. 2798-2813
Keywords [en]
Least squares, system identification
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-255416DOI: 10.1109/TAC.2018.2877673ISI: 000473489700011Scopus ID: 2-s2.0-85055726363OAI: oai:DiVA.org:kth-255416DiVA, id: diva2:1343065
Note

QC 20190815

Available from: 2019-08-15 Created: 2019-08-15 Last updated: 2019-10-15Bibliographically approved

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Galrinho, MiguelRojas, Cristian R.Hjalmarsson, Håkan

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