Research output per year
Research output per year
Baptiste Sinquin, Michel Verhaegen
Research output: Contribution to journal › Article › Scientific › peer-review
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 language | English |
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Article number | 8375680 |
Pages (from-to) | 448-463 |
Journal | IEEE Transactions on Automatic Control |
Volume | 64 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2019 |
Research output: Thesis › Dissertation (TU Delft)