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Regularized linear system identification using atomic, nuclear and kernel-based norms: The role of the stability constraint
University of Padua, Italy.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-8655-2655
University of Padua, Italy.
University of Pavia, Italy.
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2016 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 69, 137-149 p.Article in journal (Refereed) PublishedText
Abstract [en]

Inspired by ideas taken from the machine learning literature, new regularization techniques have been recently introduced in linear system identification. In particular, all the adopted estimators solve a regularized least squares problem, differing in the nature of the penalty term assigned to the impulse response. Popular choices include atomic and nuclear norms (applied to Hankel matrices) as well as norms induced by the so called stable spline kernels. In this paper, a comparative study of estimators based on these different types of regularizers is reported. Our findings reveal that stable spline kernels outperform approaches based on atomic and nuclear norms since they suitably embed information on impulse response stability and smoothness. This point is illustrated using the Bayesian interpretation of regularization. We also design a new class of regularizers defined by "integral" versions of stable spline/TC kernels. Under quite realistic experimental conditions, the new estimators outperform classical prediction error methods also when the latter are equipped with an oracle for model order selection. (C) 2016 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
PERGAMON-ELSEVIER SCIENCE LTD , 2016. Vol. 69, 137-149 p.
Keyword [en]
Linear system identification; Kernel-based regularization; Atomic and nuclear norms; Hankel operator; Lasso; Bayesian interpretation of regularization; Gaussian processes; Reproducing kernel Hilbert spaces
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-130057DOI: 10.1016/j.automatica.2016.02.012ISI: 000377312800015OAI: diva2:947042

Funding Agencies|MIUR FIRB project [RBFR12M3AC]; Progetto di Ateneo [CPDA147754/14]; Linnaeus Center CADICS; Swedish Research Council; ERC advanced grant LEARN [267381]; European Research Council; Swedish Research Council (VR) [2014-5894]

Available from: 2016-07-06 Created: 2016-07-06 Last updated: 2016-08-20

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The full text will be freely available from 2018-01-31 16:38
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Chen, TianshiLjung, Lennart
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