Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization

Wang Jian-hong

doi:doi:10.11648/j.mlr.20170201.13

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Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization

Wang Jian-hong

Published in Machine Learning Research (Volume 2, Issue 1)

Received: 10 January 2017 Accepted: 14 February 2017 Published: 2 March 2017

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Abstract

In this paper, we propose two recursive algorithms for closed loop identification under the framework of a tailor made parameterization. The closed loop transfer function is parameterized using the parameters of the open loop plant model, and utilizing knowledge of the feedback controller. When the plant model and feedback controller are all polynomial forms, a recursive least squares method with forgetting schemes is proposed to verify that this recursive method can be regarded as regularization least squares problem. Furthermore we also extend the tailor made parameterization method to nonlinear system and nonlinear controller, then an iterative least squares algorithm is applied to solve one nonlinear optimization problem.

Published in	Machine Learning Research (Volume 2, Issue 1)
DOI	10.11648/j.mlr.20170201.13
Page(s)	19-25
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

Closed Loop Identification, Tailor Made Parameterization, Recursive Algorithm, Forgetting Schemes

References

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[2]	Franky De Bruyne, “Gradient expressions for a closed loop identification scheme with a tailor made parameterization,” Automatica, vol. 35, no. 11, pp. 1867-1871, 1999.
[3]	Arne Dankers, Paul M J Vandenhof, “Errors-in-variables identification in dynamic networks-consistency results for an instrumental variable approach,” Automatica, vol. 62, no. 12, pp. 39-50, 2015.
[4]	Mathieu Pouliquen, Olivier Gehan, “Bounded error identification for closed loop systems,” Automatica, vol. 50, no. 7, pp. 1884-1890, 2014.
[5]	Ljung, L, “System identification: Theory for the user,” Prentice Hall, 1999.
[6]	Urban Forssel, Lennart Ljung, “Closed loop identification revisted,” Automatica, vol. 35, no. 7, pp. 1215-1241, 1999.
[7]	Per Hagg, Johan Schoukens, “The transient impulse response modeling method for non-parametric system identification,” Automatica, vol. 68, no. 6, pp. 314-328, 2016.
[8]	Kaushik Mahata, Johan Schoukens, “Information matrix and D-optimal design with Gaussian inputs for Wiener model identification,” Automatica, vol. 69, no. 7, pp. 65-77, 2016.
[9]	Hakan Hjalmarsson, Brett Ninness, “Least squares estimation of a class of frequency functions: a finite sample variance expression,” Automatica, vol. 42, no. 2, pp. 589-600, 2006.
[10]	G. Pillonetto, “Kernel methods in system identification, machine learning and function estimation: a survey,” Automatica., vol. 50, pp. 657–682, Mar. 2013.
[11]	Brett Ninness, “On the CRLB for combined model and model order estimation of stationary stochastic process,” IEEE Signal Processing Letters, vol. 11, no. 2, pp. 293-297, 2004.

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Wang Jian-hong. (2017). Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization. Machine Learning Research, 2(1), 19-25. https://doi.org/10.11648/j.mlr.20170201.13

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ACS Style

Wang Jian-hong. Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization. Mach. Learn. Res. 2017, 2(1), 19-25. doi: 10.11648/j.mlr.20170201.13

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AMA Style

Wang Jian-hong. Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization. Mach Learn Res. 2017;2(1):19-25. doi: 10.11648/j.mlr.20170201.13

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@article{10.11648/j.mlr.20170201.13,
  author = {Wang Jian-hong},
  title = {Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization},
  journal = {Machine Learning Research},
  volume = {2},
  number = {1},
  pages = {19-25},
  doi = {10.11648/j.mlr.20170201.13},
  url = {https://doi.org/10.11648/j.mlr.20170201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20170201.13},
  abstract = {In this paper, we propose two recursive algorithms for closed loop identification under the framework of a tailor made parameterization. The closed loop transfer function is parameterized using the parameters of the open loop plant model, and utilizing knowledge of the feedback controller. When the plant model and feedback controller are all polynomial forms, a recursive least squares method with forgetting schemes is proposed to verify that this recursive method can be regarded as regularization least squares problem. Furthermore we also extend the tailor made parameterization method to nonlinear system and nonlinear controller, then an iterative least squares algorithm is applied to solve one nonlinear optimization problem.},
 year = {2017}
}

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TY  - JOUR
T1  - Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization
AU  - Wang Jian-hong
Y1  - 2017/03/02
PY  - 2017
N1  - https://doi.org/10.11648/j.mlr.20170201.13
DO  - 10.11648/j.mlr.20170201.13
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 19
EP  - 25
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20170201.13
AB  - In this paper, we propose two recursive algorithms for closed loop identification under the framework of a tailor made parameterization. The closed loop transfer function is parameterized using the parameters of the open loop plant model, and utilizing knowledge of the feedback controller. When the plant model and feedback controller are all polynomial forms, a recursive least squares method with forgetting schemes is proposed to verify that this recursive method can be regarded as regularization least squares problem. Furthermore we also extend the tailor made parameterization method to nonlinear system and nonlinear controller, then an iterative least squares algorithm is applied to solve one nonlinear optimization problem.
VL  - 2
IS  - 1
ER  -

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Author Information

Wang Jian-hong

School of Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute, Jingdezhen, China

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APA Style

Wang Jian-hong. (2017). Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization. Machine Learning Research, 2(1), 19-25. https://doi.org/10.11648/j.mlr.20170201.13

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ACS Style

Wang Jian-hong. Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization. Mach. Learn. Res. 2017, 2(1), 19-25. doi: 10.11648/j.mlr.20170201.13

Copy | Download

AMA Style

Wang Jian-hong. Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization. Mach Learn Res. 2017;2(1):19-25. doi: 10.11648/j.mlr.20170201.13

Copy | Download

@article{10.11648/j.mlr.20170201.13,
  author = {Wang Jian-hong},
  title = {Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization},
  journal = {Machine Learning Research},
  volume = {2},
  number = {1},
  pages = {19-25},
  doi = {10.11648/j.mlr.20170201.13},
  url = {https://doi.org/10.11648/j.mlr.20170201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20170201.13},
  abstract = {In this paper, we propose two recursive algorithms for closed loop identification under the framework of a tailor made parameterization. The closed loop transfer function is parameterized using the parameters of the open loop plant model, and utilizing knowledge of the feedback controller. When the plant model and feedback controller are all polynomial forms, a recursive least squares method with forgetting schemes is proposed to verify that this recursive method can be regarded as regularization least squares problem. Furthermore we also extend the tailor made parameterization method to nonlinear system and nonlinear controller, then an iterative least squares algorithm is applied to solve one nonlinear optimization problem.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization
AU  - Wang Jian-hong
Y1  - 2017/03/02
PY  - 2017
N1  - https://doi.org/10.11648/j.mlr.20170201.13
DO  - 10.11648/j.mlr.20170201.13
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 19
EP  - 25
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20170201.13
AB  - In this paper, we propose two recursive algorithms for closed loop identification under the framework of a tailor made parameterization. The closed loop transfer function is parameterized using the parameters of the open loop plant model, and utilizing knowledge of the feedback controller. When the plant model and feedback controller are all polynomial forms, a recursive least squares method with forgetting schemes is proposed to verify that this recursive method can be regarded as regularization least squares problem. Furthermore we also extend the tailor made parameterization method to nonlinear system and nonlinear controller, then an iterative least squares algorithm is applied to solve one nonlinear optimization problem.
VL  - 2
IS  - 1
ER  -

Copy | Download