Kronecker-ARX models in identifying (2D) spatial-temporal systems

B. Sinquin; M. Verhaegen

doi:10.1016/j.ifacol.2017.08.1855

Kronecker-ARX models in identifying (2D) spatial-temporal systems

Team Raf Van de Plas

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

In this paper we address the identification of (2D) spatial-temporal dynamical systems governed by the Vector Auto-Regressive (VAR) form. The coefficient-matrices of the VAR model are parametrized as sums of Kronecker products. When the number of terms in the sum is small compared to the size of the matrix, such a Kronecker representation leads to high data compression. Estimating in least-squares sense the coefficient-matrices gives rise to a bilinear estimation problem, which is tackled using a three-stage algorithm. A numerical example demonstrates the advantages of the new modeling paradigm. It leads to comparable performances with the unstructured least-squares estimation of VAR models. However, the number of parameters in the new modeling paradigm grows linearly w.r.t. the number of nodes in the 2D sensor network instead of quadratically in the full unstructured matrix case.

Original language	English
Title of host publication	IFAC-PapersOnLine
Subtitle of host publication	Proceedings 20th IFAC World Congress
Editors	Denis Dochain, Didier Henrion, Dimitri Peaucelle
Place of Publication	Laxenburg, Austria
Publisher	Elsevier
Pages	14131-14136
Volume	50-1
DOIs	https://doi.org/10.1016/j.ifacol.2017.08.1855
Publication status	Published - 2017
Event	20th World Congress of the International Federation of Automatic Control (IFAC), 2017 - Toulouse, France Duration: 9 Jul 2017 → 14 Jul 2017 Conference number: 20 https://www.ifac2017.org

Publication series

Name	IFAC-PapersOnLine
Number	1
Volume	50

Conference

Conference	20th World Congress of the International Federation of Automatic Control (IFAC), 2017
Abbreviated title	IFAC 2017
Country/Territory	France
City	Toulouse
Period	9/07/17 → 14/07/17
Internet address	https://www.ifac2017.org

Keywords

2D large-scale systems
Kronecker product
low-rank approximation
Vector AutoRegressive model

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10.1016/j.ifacol.2017.08.1855

1-s2.0-S2405896317324801-mainFinal published version, 450 KB

Cite this

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title = "Kronecker-ARX models in identifying (2D) spatial-temporal systems",

abstract = "In this paper we address the identification of (2D) spatial-temporal dynamical systems governed by the Vector Auto-Regressive (VAR) form. The coefficient-matrices of the VAR model are parametrized as sums of Kronecker products. When the number of terms in the sum is small compared to the size of the matrix, such a Kronecker representation leads to high data compression. Estimating in least-squares sense the coefficient-matrices gives rise to a bilinear estimation problem, which is tackled using a three-stage algorithm. A numerical example demonstrates the advantages of the new modeling paradigm. It leads to comparable performances with the unstructured least-squares estimation of VAR models. However, the number of parameters in the new modeling paradigm grows linearly w.r.t. the number of nodes in the 2D sensor network instead of quadratically in the full unstructured matrix case.",

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booktitle = "IFAC-PapersOnLine",

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Sinquin, B & Verhaegen, M 2017, Kronecker-ARX models in identifying (2D) spatial-temporal systems. in D Dochain, D Henrion & D Peaucelle (eds), IFAC-PapersOnLine: Proceedings 20th IFAC World Congress. vol. 50-1, IFAC-PapersOnLine, no. 1, vol. 50, Elsevier, Laxenburg, Austria, pp. 14131-14136, 20th World Congress of the International Federation of Automatic Control (IFAC), 2017, Toulouse, France, 9/07/17. https://doi.org/10.1016/j.ifacol.2017.08.1855

Kronecker-ARX models in identifying (2D) spatial-temporal systems. / Sinquin, B.; Verhaegen, M.
IFAC-PapersOnLine: Proceedings 20th IFAC World Congress. ed. / Denis Dochain; Didier Henrion; Dimitri Peaucelle. Vol. 50-1 Laxenburg, Austria: Elsevier, 2017. p. 14131-14136 (IFAC-PapersOnLine; Vol. 50, No. 1).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AU - Sinquin, B.

AU - Verhaegen, M.

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PY - 2017

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N2 - In this paper we address the identification of (2D) spatial-temporal dynamical systems governed by the Vector Auto-Regressive (VAR) form. The coefficient-matrices of the VAR model are parametrized as sums of Kronecker products. When the number of terms in the sum is small compared to the size of the matrix, such a Kronecker representation leads to high data compression. Estimating in least-squares sense the coefficient-matrices gives rise to a bilinear estimation problem, which is tackled using a three-stage algorithm. A numerical example demonstrates the advantages of the new modeling paradigm. It leads to comparable performances with the unstructured least-squares estimation of VAR models. However, the number of parameters in the new modeling paradigm grows linearly w.r.t. the number of nodes in the 2D sensor network instead of quadratically in the full unstructured matrix case.

AB - In this paper we address the identification of (2D) spatial-temporal dynamical systems governed by the Vector Auto-Regressive (VAR) form. The coefficient-matrices of the VAR model are parametrized as sums of Kronecker products. When the number of terms in the sum is small compared to the size of the matrix, such a Kronecker representation leads to high data compression. Estimating in least-squares sense the coefficient-matrices gives rise to a bilinear estimation problem, which is tackled using a three-stage algorithm. A numerical example demonstrates the advantages of the new modeling paradigm. It leads to comparable performances with the unstructured least-squares estimation of VAR models. However, the number of parameters in the new modeling paradigm grows linearly w.r.t. the number of nodes in the 2D sensor network instead of quadratically in the full unstructured matrix case.

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KW - Vector AutoRegressive model

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A2 - Dochain, Denis

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PB - Elsevier

CY - Laxenburg, Austria

T2 - 20th World Congress of the International Federation of Automatic Control (IFAC), 2017

Y2 - 9 July 2017 through 14 July 2017

ER -

Kronecker-ARX models in identifying (2D) spatial-temporal systems

Abstract

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Keywords

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Structured matrices for predictive control of large and multi-dimensional systems

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