Recursive Identification of Hammerstein Systems with Polynomial Function Approximation

Wang Jian-hong; Tang De-zhi; Jiang Hong; Tang Xiao-jun

doi:doi:10.11648/j.ijmfs.20170306.12

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Recursive Identification of Hammerstein Systems with Polynomial Function Approximation

Wang Jian-hong, Tang De-zhi, Jiang Hong, Tang Xiao-jun

Published in International Journal of Management and Fuzzy Systems (Volume 3, Issue 6)

Received: 25 September 2017 Accepted: 27 October 2017 Published: 20 November 2017

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Abstract

Nonlinear system identification is considered, where the nonlinear static function was approximated by a number of polynomial functions. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The identification procedure is divided into two steps. Firstly we adopt the extended stochastic gradient algorithm to identify some unknown parameters. Secondly using singular value decomposition (SVD), we propose a new method to identify other parameters. The basic idea is to replace un-measurable noise terms in the information vectors by their estimates, and to compute the noise estimates based on the obtained parameter estimates. The applicability of the approach is illustrated by a simulation.

Published in	International Journal of Management and Fuzzy Systems (Volume 3, Issue 6)
DOI	10.11648/j.ijmfs.20170306.12
Page(s)	87-94
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Nonlinear System, Hammerstein Systems, Polynomial Functions Approximation, Recursive Identification, Singular Value Decomposition

References

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[2]	Lennart Ljung. System Identification: Theory for the user [M], Prentice-Hall, Upper Saddle River, 1999.
[3]	Martin Enqvist, Lennart Ljung. Linear approximations of nonlinear FIR systems for separable input processes. Automatica [J], 2005. 41(3):459-473.
[4]	J. J. Bussgang. Cross correlate on functions of amplitude-distorted Gaussian signals. Technical Report Technical report 216, MIT Laboratory of Electronics, 1952.
[5]	Bai E-W. Frequency domain identification of Hammerstein models[J]. IEEE transactions on automatic control. 2003. 48(4):530-541.
[6]	Bai E-W. A random least-trimmed-squares identification algorithm [J]. Automatica. 2003. 39(9): 1651-1659.
[7]	Bai E-W. Identification of linear systems with hard input nonlinearities of known structure [J]. Automatica, 2002. 38(5): 853-860.
[8]	Lennart Ljung. Estimating linear time invariant models of non-linear time-varying system [J]. European Journal of Control, 2001. 7 (2):203-219.
[9]	R. Pintelon, J. Schoukens. Fast approximation identification of nonlinear systems [J]. Automatica, 2003. 39(7):1267-1273.
[10]	Ding F, Tongwen Chen. Identification of Hammerstein nonlinear ARMAX systems [J]. Automatica, 2005. 41 (9):1479-1489.
[11]	Ding F, Tongwen Chen. Performance analysis of multi-innovation gradient type identification methods [J]. Automatica, 2007. 43(1):1-14.
[12]	Wang DQ, Ding F. Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems [J]. Computers & Mathematics with Applications, 2008. 56(12): 3157-3164.

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APA Style

Wang Jian-hong, Tang De-zhi, Jiang Hong, Tang Xiao-jun. (2017). Recursive Identification of Hammerstein Systems with Polynomial Function Approximation. International Journal of Management and Fuzzy Systems, 3(6), 87-94. https://doi.org/10.11648/j.ijmfs.20170306.12

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ACS Style

Wang Jian-hong; Tang De-zhi; Jiang Hong; Tang Xiao-jun. Recursive Identification of Hammerstein Systems with Polynomial Function Approximation. Int. J. Manag. Fuzzy Syst. 2017, 3(6), 87-94. doi: 10.11648/j.ijmfs.20170306.12

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AMA Style

Wang Jian-hong, Tang De-zhi, Jiang Hong, Tang Xiao-jun. Recursive Identification of Hammerstein Systems with Polynomial Function Approximation. Int J Manag Fuzzy Syst. 2017;3(6):87-94. doi: 10.11648/j.ijmfs.20170306.12

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@article{10.11648/j.ijmfs.20170306.12,
  author = {Wang Jian-hong and Tang De-zhi and Jiang Hong and Tang Xiao-jun},
  title = {Recursive Identification of Hammerstein Systems with Polynomial Function Approximation},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {3},
  number = {6},
  pages = {87-94},
  doi = {10.11648/j.ijmfs.20170306.12},
  url = {https://doi.org/10.11648/j.ijmfs.20170306.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20170306.12},
  abstract = {Nonlinear system identification is considered, where the nonlinear static function was approximated by a number of polynomial functions. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The identification procedure is divided into two steps. Firstly we adopt the extended stochastic gradient algorithm to identify some unknown parameters. Secondly using singular value decomposition (SVD), we propose a new method to identify other parameters. The basic idea is to replace un-measurable noise terms in the information vectors by their estimates, and to compute the noise estimates based on the obtained parameter estimates. The applicability of the approach is illustrated by a simulation.},
 year = {2017}
}

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TY  - JOUR
T1  - Recursive Identification of Hammerstein Systems with Polynomial Function Approximation
AU  - Wang Jian-hong
AU  - Tang De-zhi
AU  - Jiang Hong
AU  - Tang Xiao-jun
Y1  - 2017/11/20
PY  - 2017
N1  - https://doi.org/10.11648/j.ijmfs.20170306.12
DO  - 10.11648/j.ijmfs.20170306.12
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 87
EP  - 94
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20170306.12
AB  - Nonlinear system identification is considered, where the nonlinear static function was approximated by a number of polynomial functions. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The identification procedure is divided into two steps. Firstly we adopt the extended stochastic gradient algorithm to identify some unknown parameters. Secondly using singular value decomposition (SVD), we propose a new method to identify other parameters. The basic idea is to replace un-measurable noise terms in the information vectors by their estimates, and to compute the noise estimates based on the obtained parameter estimates. The applicability of the approach is illustrated by a simulation.
VL  - 3
IS  - 6
ER  -

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Author Information

Wang Jian-hong

School of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, China
Tang De-zhi

School of Electrical and Information Engineering, Anhui University of Technology, Ma-an-shan, China
Jiang Hong

School of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, China
Tang Xiao-jun

School of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, China

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Plain Text BibTeX RIS

APA Style

Wang Jian-hong, Tang De-zhi, Jiang Hong, Tang Xiao-jun. (2017). Recursive Identification of Hammerstein Systems with Polynomial Function Approximation. International Journal of Management and Fuzzy Systems, 3(6), 87-94. https://doi.org/10.11648/j.ijmfs.20170306.12

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ACS Style

Wang Jian-hong; Tang De-zhi; Jiang Hong; Tang Xiao-jun. Recursive Identification of Hammerstein Systems with Polynomial Function Approximation. Int. J. Manag. Fuzzy Syst. 2017, 3(6), 87-94. doi: 10.11648/j.ijmfs.20170306.12

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AMA Style

Wang Jian-hong, Tang De-zhi, Jiang Hong, Tang Xiao-jun. Recursive Identification of Hammerstein Systems with Polynomial Function Approximation. Int J Manag Fuzzy Syst. 2017;3(6):87-94. doi: 10.11648/j.ijmfs.20170306.12

Copy | Download

@article{10.11648/j.ijmfs.20170306.12,
  author = {Wang Jian-hong and Tang De-zhi and Jiang Hong and Tang Xiao-jun},
  title = {Recursive Identification of Hammerstein Systems with Polynomial Function Approximation},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {3},
  number = {6},
  pages = {87-94},
  doi = {10.11648/j.ijmfs.20170306.12},
  url = {https://doi.org/10.11648/j.ijmfs.20170306.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20170306.12},
  abstract = {Nonlinear system identification is considered, where the nonlinear static function was approximated by a number of polynomial functions. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The identification procedure is divided into two steps. Firstly we adopt the extended stochastic gradient algorithm to identify some unknown parameters. Secondly using singular value decomposition (SVD), we propose a new method to identify other parameters. The basic idea is to replace un-measurable noise terms in the information vectors by their estimates, and to compute the noise estimates based on the obtained parameter estimates. The applicability of the approach is illustrated by a simulation.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Recursive Identification of Hammerstein Systems with Polynomial Function Approximation
AU  - Wang Jian-hong
AU  - Tang De-zhi
AU  - Jiang Hong
AU  - Tang Xiao-jun
Y1  - 2017/11/20
PY  - 2017
N1  - https://doi.org/10.11648/j.ijmfs.20170306.12
DO  - 10.11648/j.ijmfs.20170306.12
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 87
EP  - 94
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20170306.12
AB  - Nonlinear system identification is considered, where the nonlinear static function was approximated by a number of polynomial functions. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The identification procedure is divided into two steps. Firstly we adopt the extended stochastic gradient algorithm to identify some unknown parameters. Secondly using singular value decomposition (SVD), we propose a new method to identify other parameters. The basic idea is to replace un-measurable noise terms in the information vectors by their estimates, and to compute the noise estimates based on the obtained parameter estimates. The applicability of the approach is illustrated by a simulation.
VL  - 3
IS  - 6
ER  -

Copy | Download