@inproceedings{Usevich14conf-Decomposing,
author = {K. Usevich},
title = {Decomposing multivariate polynomials with structured low-rank matrix completion},
booktitle = {Proc. 21th Int. Symposium on Mathematical Theory of Networks and Systems},
year = {2014},
pages = {1826--1833},
abstract = {We are focused on numerical methods for decomposing a multivariate polynomial as a sum of univariate polynomials in linear forms. The main tool is the recent result on correspondence between the Waring rank of a homogeneous polynomial and the rank of a partially known quasi-Hankel matrix constructed from the coefficients of the polynomial. Based on this correspondence, we show that the original decomposition problem can be reformulated as structured low-rank matrix completion (or as structured low-rank approximation in the case of approximate decomposition). We construct algorithms for the polynomial decomposition problem. In the case of bivariate polynomials, we provide an extension of the well-known Sylvester algorithm for binary forms.},
pdf = {http://www.gipsa-lab.grenoble-inp.fr/~konstantin.usevich/_preprints/Usevich14conf-Decomposing.pdf}
}
@inproceedings{VanMulders.etal14conf-Identification,
author = {A. {Van Mulders} and L. Vanbeylen and K. Usevich},
title = {Identification of a block-structured model with several sources of nonlinearity},
booktitle = {Proc. 14th European Control Conf.},
year = {2014},
abstract = {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 polynomial nonlinearities connected to a Multiple-Input Multiple-Output (MIMO) dynamic part. The presented method is an extension and improvement of prior work, where at most two nonlinearities could be identified. The location of the nonlinearities or their relation to other parts of the model does not have to be known beforehand: the method is a black-box approach, in which no states, internal signals or structural properties need to be measured or known. The first step is to estimate a partly structured polynomial (nonlinear) state-space model from input-output measurements. Secondly, an algebraic approach is used to split the dynamics and the nonlinearities by decomposing the multivariate polynomial coefficients.},
pages = {1717--1722},
doi = {10.1109/ECC.2014.6862455},
pdf = {http://www.gipsa-lab.grenoble-inp.fr/~konstantin.usevich/_preprints/VanMulders.etal14conf-Identification.pdf}
}
@inproceedings{DreIshSch15c1,
author = {P. Dreesen and M. Ishteva and J. Schoukens},
title = {Recovering {W}iener-{H}ammerstein nonlinear state-space models using linear algebra},
booktitle = {Proc. 17th IFAC Symposium on System Identification},
volume = {48(28)},
pages = {951--956},
year = {2015},
doi = {http://dx.doi.org/10.1016/j.ifacol.2015.12.253},
address = {Beijing, China},
pdf = {http://homepages.vub.ac.be/~mishteva/papers/sysid2015_recovering_WH_models.pdf}
}
@inproceedings{DreIshSch15c2,
author = {P. Dreesen and M. Ishteva and J. Schoukens},
title = {On the full and block-decoupling of nonlinear functions},
booktitle = {PAMM-Proceedings of Applied Mathematics and Mechanics},
year = {2015},
volume = {15},
number = {1},
pages = {739--742},
issn = {1617-7061},
url = {http://dx.doi.org/10.1002/pamm.201510352},
pdf = {http://homepages.vub.ac.be/~mishteva/papers/On_the_full_and_block-decoupling_of_nonlinear_functions_PAMM_2015.pdf},
doi = {10.1002/pamm.201510352}
}
@inproceedings{dreesen2017camsap,
author = {P. Dreesen and K. Tiels and M. Ishteva and J. Schoukens},
title = {Nonlinear system identification: finding structure in nonlinear black-box models},
year = {2017},
booktitle = {Proc. IEEE Int. Workshop on Computational Advances in Multi-Sensor Adaptive Processing},
pages = {443--446}
}
@inproceedings{westwick2017ifac,
author = {D. Westwick and M. Ishteva and P. Dreesen and J. Schoukens},
title = {Tensor factorization based estimates of parallel {W}iener-{H}ammerstein models},
booktitle = {Proc. IFAC World Congress},
volume = {50},
number = {1},
pages = {9468--9473},
year = {2017}
}
@inproceedings{dreesen2016isma,
author = {P. Dreesen and A. {Fakhrizadeh Esfahani} and J. Stoev and K. Tiels and J. Schoukens},
title = {Decoupling nonlinear state-space models: case studies},
booktitle = {Int. Conf. on Noise and Vibration, Leuven, Belgium},
year = {2016},
editor = {P. Sas and D. Moens and A. van de Walle},
pages = {2639--2646}
}
@inproceedings{hollander2016isma,
author = {G. Hollander and P. Dreesen and M. Ishteva and J. Schoukens},
title = {Parallel {W}iener-{H}ammerstein identification: A case study},
editor = {P. Sas and D. Moens and A. van de Walle},
booktitle = {Int. Conf. on Noise and Vibration},
year = {2016},
pages = {2647--2656}
}
@inproceedings{dreesen2015sysid,
author = {P. Dreesen and M. Ishteva and J. Schoukens},
title = {Recovering {W}iener-{H}ammerstein nonlinear state-space models using linear algebra},
booktitle = {Proc. IFAC World Congress},
volume = {48},
number = {28},
pages = {951--956},
year = {2015},
issn = {2405-8963},
doi = {http://dx.doi.org/10.1016/j.ifacol.2015.12.253},
booktitle = {Proc. 17th {IFAC} Symp. Syst. Ident.},
address = {Beijing, China}
}
@inproceedings{dreesen2015i2mtc,
title = {Decoupling Static Nonlinearities in a Parallel {W}iener-{H}ammerstein System: A First-order Approach},
author = {P. Dreesen and M. Schoukens and K. Tiels and J. Schoukens},
year = {2015},
booktitle = {Proc. {IEEE} Int. Conf. on Instrumentation and Measurement Technology},
pages = {987--992}
}
@inproceedings{ica2,
author = {I. Markovsky and O. Debals and L. De Lathauwer},
title = {Sum-of-Exponentials Modeling and Common Dynamics Estimation Using Tensorlab},
year = {2017},
booktitle = {Proc. 20th IFAC World Congress},
month = {July},
pages = {14715--14720},
address = {Toulouse, France},
pdf = {http://homepages.vub.ac.be/~imarkovs/publications/ica2.pdf},
abstract = {Fitting a signal to a sum-of-exponentials model is a basic problem in signal processing. It can be posed and solved as a Hankel structured low-rank matrix approximation problem. Subsequently, local optimization, subspace, and convex relaxation methods can be used for the numerical solution. In this paper, we show another approach, based on the recently proposed concept of structured data fusion. Structured data fusion problems are solved in the Tensorlab toolbox by local optimization methods. The approach allows fitting of signals with missing samples and adding constraints on the model, such as fixed exponents and common dynamics in multi-channel estimation problems. These problems are non-trivial to solve by other existing methods.},
keywords = {system identification; low-rank approximation; mosaic Hankel matrix; tensorlab; structured data fusion.}
}
@inproceedings{med2,
author = {I. Markovsky},
title = {Application of low-rank approximation for nonlinear system identification},
year = {2017},
booktitle = {Proc. 25th IEEE Mediterranean Conf. on Control and Automation},
month = {July},
address = {Valletta, Malta},
pdf = {http://homepages.vub.ac.be/~imarkovs/publications/med2.pdf},
abstract = {The paper considers the class of discrete-time, single-input, single-output, nonlinear dynamical systems described by a polynomial difference equation. This class, call polynomial time-invariant, is a proper generalization of the linear time-invariant model class. The identification data is assumed to be generated in the errors-in-variables setting, where the input and the output noise is zero mean, white, and the noise variances is known up to a scaling factor. The identification problem has two sub-problems
\begin{enumerate}
\item structure selection: find the monomials appearing in the difference equation representation of the system, and
\item parameter estimation: estimate the coefficients of the equation.
\end{enumerate}
The main result shows that the parameter estimation by minimization of the 2-norm of the equation error leads to unstructured low-rank approximation of an extended data matrix. The resulting method is computationally robust and efficient due to the use of the singular value decomposition. However, it requires knowledge of the model structure and even when the correct model structure is used, it leads to biased results. For the structure selection, the use 1-norm regularization is proposed. For the bias removal an adjustment of the ordinary least squares estimator is proposed. The resulting adjusted low-rank approximation methods defines an unbiased estimator for the model parameters of the polynomial time-invariant model. },
isbn = {978-1-5090-4532-7/17},
pages = {12--16}
}
@inproceedings{dreesen2018lvaica,
author = {P. Dreesen and J. {De Geeter} and M. Ishteva},
title = {Decoupling multivariate functions using second-order information and tensors},
booktitle = {Proc. 14th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA 2018)},
series = {Lecture Notes on Computer Science (LNCS)},
volume = {10891},
editor = {Y. Deville and S. Gannot and R. Mason and M.~D. Plumbley and D. Ward},
pages = {79--88},
address = {Guildford, UK},
year = {2018},
doi = {10.1007/978-3-319-93764-9_8},
url = {https://arxiv.org/abs/1805.08479}
}
@inproceedings{fakhrizadeh2017ifac,
author = {A. Fakhrizadeh Esfahani and P. Dreesen and K. Tiels and J.-P. No\"el and J. Schoukens},
title = {Polynomial state-space model decoupling for the identification of hysteretic systems},
series = {IFAC-PapersOnLine},
volume = {50(1)},
pages = {458--463},
year = {2017},
doi = {10.1016/j.ifacol.2017.08.082},
booktitle = {Proc. {IFAC} 2017 World Congress},
address = {Toulouse, France},
myurl = {./pub/fakhrizadeh2017ifac.pdf}
}
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