# Low-rank tensor recovery for Jacobian-based Volterra identification of parallel Wiener-Hammerstein systems

@article{Usevich2021LowrankTR, title={Low-rank tensor recovery for Jacobian-based Volterra identification of parallel Wiener-Hammerstein systems}, author={Konstantin Usevich and Philippe Dreesen and Mariya Ishteva}, journal={IFAC-PapersOnLine}, year={2021} }

We consider the problem of identifying a parallel Wiener-Hammerstein structure from Volterra kernels. Methods based on Volterra kernels typically resort to coupled tensor decompositions of the kernels. However, in the case of parallel Wiener-Hammerstein systems, such methods require nontrivial constraints on the factors of the decompositions. In this paper, we propose an entirely different approach: by using special sampling (operating) points for the Jacobian of the nonlinear map from past…

#### One Citation

Parameter Estimation of Parallel Wiener-Hammerstein Systems by Decoupling their Volterra Representations

- MathematicsIFAC-PapersOnLine
- 2021

Abstract Nonlinear dynamic systems are often approximated by a Volterra series, which is a generalization of the Taylor series for systems with memory. However, the Volterra series lacks physical…

#### References

SHOWING 1-10 OF 30 REFERENCES

Tensor Factorization based Estimates of Parallel Wiener Hammerstein Models

- Mathematics
- 2017

Abstract Factoring the third-order Volterra kernel of a Wiener-Hammerstein model to recover the impulse responses of its two constituent linear systems is a common example in the multilinear algebra…

Modeling Parallel Wiener-Hammerstein Systems Using Tensor Decomposition of Volterra Kernels

- Computer ScienceLVA/ICA
- 2017

This work illustrates how the parallel Wiener-Hammerstein block-structure gives rise to a joint tensor decomposition of the Volterra kernels with block-circulant structured factors, and concludes that the combination of VolterRA kernels and tensor methods is a fruitful way to tackle the parallelWiener- Hammerstein system identification task.

Parameter Estimation of Parallel Wiener-Hammerstein Systems by Decoupling their Volterra Representations

- MathematicsIFAC-PapersOnLine
- 2021

Abstract Nonlinear dynamic systems are often approximated by a Volterra series, which is a generalization of the Taylor series for systems with memory. However, the Volterra series lacks physical…

Toeplitz–Vandermonde Matrix Factorization With Application to Parameter Estimation of Wiener–Hammerstein Systems

- Mathematics, Computer ScienceIEEE Signal Processing Letters
- 2007

This algorithm is used for estimating nondiagonal coefficients of Volterra kernels associated with a Wiener-Hammerstein system and is constituted by a set of recurrence relations derived when the matrix to be decomposed has at least three columns.

Decoupling Multivariate Polynomials Using First-Order Information and Tensor Decompositions

- Computer Science, MathematicsSIAM J. Matrix Anal. Appl.
- 2015

The canonical polyadic decomposition of the three-way tensor of Jacobian matrices directly returns the unknown linear relations as well as the necessary information to reconstruct the univariate polynomials.

Decoupling Multivariate Functions Using Second-Order Information and Tensors

- Computer Science, MathematicsLVA/ICA
- 2018

This article generalizes a tensor-based method for performing decomposition of multivariate vector functions and studies how the use of second-order derivative information can be incorporated, to push the method towards more involved configurations, while preserving uniqueness of the underlying tensor decompositions.

Regularized nonparametric Volterra kernel estimation

- Mathematics, Computer ScienceAutom.
- 2017

Abstract In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modeled as Volterra series.…

Tensor Decompositions and Applications

- Mathematics, Computer ScienceSIAM Rev.
- 2009

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order…

Tensors : A brief introduction

- Mathematics, Computer ScienceIEEE Signal Processing Magazine
- 2014

Tensor decompositions are at the core of many blind source separation (BSS) algorithms, either explicitly or implicitly, and plays a central role in the identification of underdetermined mixtures.

Identification of a block-structured model with several sources of nonlinearity

- Mathematics, Computer Science2014 European Control Conference (ECC)
- 2014

This paper focuses on a state-space based approach for the identification of a rather general nonlinear block-structured model. The model has several Single-Input Single-Output (SISO) static…