Research Output per year

### Abstract

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 |

### Keywords

- 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

## Fingerprint Dive into the research topics of 'QUARKS: Identification of large-scale Kronecker vector-autoregressive models'. Together they form a unique fingerprint.

## Research Output

- 4 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: Thesis › Dissertation (TU Delft)

## Cite this

*IEEE Transactions on Automatic Control*,

*64*(2), 448-463. [8375680]. https://doi.org/10.1109/TAC.2018.2845662