Tensor Network alternating linear scheme for MIMO Volterra system identification

Batselier, Kim; Chen, Zhongming; Wong, Ngai

doi:10.1016/j.automatica.2017.06.033

Cited by 55 publications

(93 citation statements)

References 30 publications

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“…This orthogonalisation is also performed on the initialisation of the cores. We refer to Oseledets (2011), Batselier et al (2017) and Chen, Batselier, Suykens, and Wong (2016) for this common step. For this orthogonalisation step, some assumptions are made on the sizes of the cores.…”

Section: Parametrisationmentioning

confidence: 99%

“…Furthermore, we also present the slightly generalised tensor network framework of Batselier et al (2017).…”

Section: Tensor Trains and Networkmentioning

confidence: 99%

“…Furthermore, in order to be able to deal with multiple output systems, we use the slightly generalised tensor network of Batselier et al (2017). This generalisation is that we allow A (1) (:, i 1 , :) to be a full matrix instead of a row vector.…”

Section: Tensor Trains and Networkmentioning

confidence: 99%

“…The optimisation of these parameters is performed using ALS for tensor networks (Batselier et al, 2017;Oseledets, 2011). That is, we start with an initialisation of the cores and iteratively update them one-by-one.…”

Section: Parametrisationmentioning

confidence: 99%

“…Namely, operations can be performed directly on the tensor network decompositions. In detail, the used class of tensor network (Batselier, Chen, & Wong, 2017) is a generalisation of tensor trains (Oseledets, 2011). They inherit tensor train efficiency results, and become tensor trains for single-output problems.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Tensor networks for MIMO LPV system identification

Gunes

Wingerden

Verhaegen

2018

International Journal of Control

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In this paper, we present a novel multiple input multiple output (MIMO) linear parameter varying (LPV) state-space refinement system identification algorithm that uses tensor networks. Its novelty mainly lies in representing the LPV sub-Markov parameters, data and state-revealing matrix condensely and in exact manner using specific tensor networks. These representations circumvent the 'curse-of-dimensionality' as they inherit the properties of tensor trains. The proposed algorithm is 'curse-of-dimensionality'-free in memory and computation and has conditioning guarantees. Its performance is illustrated using simulation cases and additionally compared with existing methods. ARTICLE HISTORY

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Section: Parametrisationmentioning

confidence: 99%

“…Furthermore, we also present the slightly generalised tensor network framework of Batselier et al (2017).…”

Section: Tensor Trains and Networkmentioning

confidence: 99%

Section: Tensor Trains and Networkmentioning

confidence: 99%

Section: Parametrisationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tensor networks for MIMO LPV system identification

Gunes

Wingerden

Verhaegen

2018

International Journal of Control

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Filtering‐based recursive least squares estimation approaches for multivariate equation‐error systems by using the multiinnovation theory

Wang

2021

Adaptive Control & Signal

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This article researches the filtering-based parameter estimation issues for a class of multivariate control systems with colored noise. A filtering-based recursive generalized extended least squares algorithm is derived, in which the data filtering technique is used for transforming the original system into two subidentification systems and the least squares principle is used for estimating parameters of these two subsystems. Furthermore, in order to improve the parameter estimation accuracy, the multiinnovation theory is added for deducing a filtering-based multiinnovation recursive generalized extended least squares algorithm.The numerical example confirms that these two proposed algorithms are effective.

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Noniterative tensor network‐based algorithm for Volterra system identification

Tan

Callafon

2022

Intl J Robust & Nonlinear

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Volterra model serves as one of the powerful alternatives to approximate nonlinear dynamics on the basis of input/output observations. The kernel representation of a Volterra model is attractive since it is linear in the kernel coefficients and always stable. Although the kernel representation suffers from the curse of dimensionality, the demand for storage requirements can be relieved via a tensor network (TN) technique. This allows one to approximate complicated coupled nonlinear dynamics with high degree and even multi-input multi-output (MIMO) Volterra models. The iterative feature of existing TN-based algorithms poses challenges for the algorithms to converge to an appropriate solution with both good prediction accuracy and minor overfitting problems. In this article, noniterative TN-based algorithms with two tuning factors to solve either a linear or ridge regression are proposed for MIMO Volterra system identification. The proposed algorithms do not suffer convergence problems due to its noniterative feature and perform active low-rank approximations to reduce overfitting problems. Simulations compare different algorithms and investigate the effects for different excitation signals.

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Tensor Network alternating linear scheme for MIMO Volterra system identification

Cited by 55 publications

References 30 publications

Tensor networks for MIMO LPV system identification

Tensor networks for MIMO LPV system identification

Filtering‐based recursive least squares estimation approaches for multivariate equation‐error systems by using the multiinnovation theory

Noniterative tensor network‐based algorithm for Volterra system identification

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