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

B. Sinquin, M. Verhaegen

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

2 Citations (Scopus)
25 Downloads (Pure)


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 languageEnglish
Title of host publicationIFAC-PapersOnLine
Subtitle of host publicationProceedings 20th IFAC World Congress
EditorsDenis Dochain, Didier Henrion, Dimitri Peaucelle
Place of PublicationLaxenburg, Austria
Publication statusPublished - 2017
Event20th World Congress of the International Federation of Automatic Control (IFAC), 2017 - Toulouse, France
Duration: 9 Jul 201714 Jul 2017
Conference number: 20

Publication series



Conference20th World Congress of the International Federation of Automatic Control (IFAC), 2017
Abbreviated titleIFAC 2017
Internet address


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

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  • Research Output

    • 2 Citations
    • 1 Dissertation (TU Delft)

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

    Sinquin, B., 8 May 2019, 219 p.

    Research output: ThesisDissertation (TU Delft)

    Open Access
  • 83 Downloads (Pure)

    Cite this

    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, pp. 14131-14136). (IFAC-PapersOnLine; Vol. 50, No. 1). Elsevier.