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

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

Sinquin, B. (TU Delft Team Raf Van de Plas)
Verhaegen, M.H.G. (TU Delft Team Raf Van de Plas)

Dochain, Denis (editor)
Henrion, Didier (editor)
Peaucelle, Dimitri (editor)

2017

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.

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

http://resolver.tudelft.nl/uuid:ec2989b9-53ac-409b-aaf6-2f6455d716e0

https://doi.org/10.1016/j.ifacol.2017.08.1855

Elsevier, Laxenburg, Austria

IFAC-PapersOnLine: Proceedings 20th IFAC World Congress, 50-1

20th World Congress of the International Federation of Automatic Control (IFAC), 2017, 2017-07-09 → 2017-07-14, Toulouse, France

IFAC-PapersOnLine, 50 (1)

Institutional Repository

conference paper

© 2017 B. Sinquin, M.H.G. Verhaegen