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Low-rank optimization in system identification
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
2019 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, the use of low-rank approximations in connection with problems in system identification is explored. Firstly, the motivation of using low-rank approximations in system identification is presented and the framework for low-rank optimization is derived. Secondly, three papers are presented where different problems in system identification are considered within the described low-rank framework. In paper A, a novel method involving the nuclear norm forestimating a Wiener model is introduced. As shown in the paper, this method performs better than existing methods in terms of finding an accurate model. In paper B and C, a group lasso framework is used to perform input selection in the model estimation which also is connected to the low rank framework. The model structures where these novel methods of input selection is used on are ARX models and state space models, respectively. As shown in the respective papers, these strategies of performing input selection perform better than existing methods in both terms of estimation and input selection.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2019. , p. 31
Series
Linköping Studies in Science and Technology. Licentiate Thesis, ISSN 0280-7971 ; 1855
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-161286DOI: 10.3384/lic.diva-161286ISBN: 9789179299743 (print)OAI: oai:DiVA.org:liu-161286DiVA, id: diva2:1366138
Presentation
2019-11-08, Ada Lovelace, B-building, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Funder
EU, European Research Council, 339681Swedish Research Council, E05946CIAvailable from: 2019-10-28 Created: 2019-10-28 Last updated: 2020-02-24Bibliographically approved
List of papers
1. Identification of the dynamics of time-varying phase aberrations from time histories of the point-spread function
Open this publication in new window or tab >>Identification of the dynamics of time-varying phase aberrations from time histories of the point-spread function
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2019 (English)In: Optical Society of America. Journal A: Optics, Image Science, and Vision, ISSN 1084-7529, E-ISSN 1520-8532, Vol. 36, no 5, p. 809-817Article in journal (Refereed) Published
Abstract [en]

To optimally compensate for time-varying phase aberrations with adaptive optics, a model of the dynamics of the aberrations is required to predict the phase aberration at the next time step. We model the time-varying behavior of a phase aberration, expressed in Zernike modes, by assuming that the temporal dynamics of the Zernike coefficients can be described by a vector-valued autoregressive (VAR) model. We propose an iterative method based on a convex heuristic for a rank-constrained optimization problem, to jointly estimate the parameters of the VAR model and the Zernike coefficients from a time series of measurements of the point-spread function (PSF) of the optical system. By assuming the phase aberration is small, the relation between aberration and PSF measurements can be approximated by a quadratic function. As such, our method is a blind identification method for linear dynamics in a stochastic Wiener system with a quadratic nonlinearity at the output and a phase retrieval method that uses a time-evolution-model constraint and a single image at every time step. (c) 2019 Optical Society of America.

Place, publisher, year, edition, pages
OPTICAL SOC AMER, 2019
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-157542 (URN)10.1364/JOSAA.36.000809 (DOI)000466360700013 ()31045008 (PubMedID)
Note

Funding Agencies|Seventh Framework Programme (FP7) [339681]; Vetenskapsradet (VR) [E05946CI]

Available from: 2019-06-22 Created: 2019-06-22 Last updated: 2019-11-27
2. Input selection in ARX model estimation using group lasso regularization
Open this publication in new window or tab >>Input selection in ARX model estimation using group lasso regularization
2018 (English)In: 18th IFAC Symposium on System Identification (SYSID), Proceedings, ELSEVIER SCIENCE BV , 2018, Vol. 51, no 15, p. 897-902Conference paper, Published paper (Refereed)
Abstract [en]

In system identification, input selection is a challenging problem. Since less complex models are desireable, non-relevant inputs should be methodically and correctly discarded before or under the estimation process. In this paper we investigate an input selection extension in least-squares ARX estimation and show that better model estimates are achieved compared to the least-square ssolution, in particular, for short batches of estimation data. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2018
Series
IFAC papers online, E-ISSN 2405-8963
Keywords
Input selection; System identification; ARX-models; ARMAX-models; Signal-to-noise ratio
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-152415 (URN)10.1016/j.ifacol.2018.09.080 (DOI)000446599200152 ()
Conference
18th IFAC Symposium on System Identification (SYSID)
Available from: 2018-10-30 Created: 2018-10-30 Last updated: 2019-10-28
3. Input selection in N2SID using group lasso regularization
Open this publication in new window or tab >>Input selection in N2SID using group lasso regularization
2017 (English)In: IFAC PAPERSONLINE, ELSEVIER SCIENCE BV , 2017, Vol. 50, no 1, p. 9474-9479Conference paper, Published paper (Refereed)
Abstract [en]

Input selection is an important and oftentimes difficult challenge in system identification. In order to achieve less complex models, irrelevant inputs should be methodically and correctly discarded before or under the estimation process. In this paper we introduce a novel method of input selection that is carried out as a natural extension in a subspace method. We show that the method robustly and accurately performs input selection at various noise levels and that it provides good model estimates. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2017
Series
IFAC PAPERSONLINE, E-ISSN 2405-8963
Keywords
Input selection; System identification; State-space models; N2SID; Subspace methods; Signal-to-noise ratio
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-145854 (URN)10.1016/j.ifacol.2017.08.1472 (DOI)000423965100077 ()
Conference
20th World Congress of the International-Federation-of-Automatic-Control (IFAC)
Note

Funding Agencies|Swedish Research Council [E05946CI]

Available from: 2018-03-21 Created: 2018-03-21 Last updated: 2019-10-31

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