QUARKS: Identification of large-scale Kronecker vector-autoregressive models

Baptiste Sinquin, Michel Verhaegen

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)


In this paper, we address the identification of two-dimensional (2-D) spatial-temporal dynamical systems described by the Vector-AutoRegressive (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 matrices, such a Kronecker representation efficiently models large-scale VAR models. Estimating the coefficient matrices in least-squares sense gives rise to a bilinear estimation problem that is tackled using an Alternating Least Squares (ALS) algorithm. Regularization or parameter constraints on the coefficient-matrices allows to induce temporal network properties, such as stability, as well as spatial properties, such as sparsity or Toeplitz structure. Convergence of the regularized ALS is proved using fixed-point theory. A numerical example demonstrates the advantages of the new modeling paradigm. It leads to comparable variance of the prediction error with the unstructured least-squares estimation of VAR models. However, the number of parameters grows only linearly with respect to the number of nodes in the 2-D sensor network instead of quadratically in the case of fully unstructured coefficient-matrices.

Original languageEnglish
Article number8375680
Pages (from-to)448-463
JournalIEEE Transactions on Automatic Control
Issue number2
Publication statusPublished - 2019


  • Adaptation models
  • Alternating Least Squares
  • Computational modeling
  • Estimation
  • Kronecker product
  • large-scale networks
  • Matrix decomposition
  • Reactive power
  • system identification
  • Tensile stress
  • Two dimensional displays
  • Vector Auto-Regressive model


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