Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation

Hong Wang-Jian; Tang De-zhi

doi:doi:10.11648/j.awcn.20170306.11

| Peer-Reviewed

Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation

Hong Wang-Jian, Tang De-zhi

Published in Advances in Wireless Communications and Networks (Volume 3, Issue 6)

Received: 5 October 2017 Accepted: 17 November 2017 Published: 5 December 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.

Published in	Advances in Wireless Communications and Networks (Volume 3, Issue 6)
DOI	10.11648/j.awcn.20170306.11
Page(s)	75-83
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), 2024. Published by Science Publishing Group

Keywords

Closed Loop Identification, Model Structure Validation, Asymptotic Region, Non-asymptotic Region

References

[1]	Robust optimal experiment design for system identification
[2]	An optimal structure selection and parameter design approach for a dual-motor-driven system used in an electric bus
[3]	The spectral parameter estimation method for parameter identification of linear fractional order systems
[4]	Subspace identification and predictive control of batch particulate processes
[5]	Urban Forssel, Lennart Ljung, “Closed loop identification revisted,” Automatica, vol. 35, no. 7, pp. 1215-1241, 1999.
[6]	Ljung, L, “System identification: Theory for the user,” Prentice Hall, 1999.
[7]	Pintelon R, Schoukens J, “System identification: a frequency domain approach,” New York: IEEE Press, 2001.
[8]	Juan C, Augero, “A virtual closed loop method for closed loop identification,” Automatica, vol 47, no. 8, pp. 1626-1637, 2011.
[9]	U, Forssell, L Ljung, “Some results on optimal experiment design,” Automatica, vol 36, no. 5, pp. 749-756, 2000.
[10]	M, Leskers, “Closed loop identification of multivariable process with part of the inputs controlled,” International Journal of Control, vol 80, no. 10, pp. 1552-1561, 2007.
[11]	Hakan Hjalmarssion, “From experiment design to closed loop control,” Automatica, vol 41, no. 3, pp. 393-438, 2005,.
[12]	Hakan Hjalmarssion, “Closed loop experiment design for linear time invariant dynamical systems via LMI,” Automatica, vol 44, no. 3, pp. 623-636, 2008.
[13]	X, Bombois, “Least costly identification experiment for control,” Automatica, vol 42, no. 10, pp. 1651-1662, 2006.
[14]	Roland Hildebrand, “Identification for control: optimal input design with respect to a worst case gap cost function,” SIAM Journal of Control Optimization, vol 41, no. 5, pp. 1586-1608, 2003.
[15]	M, Gevers, “Identification of multi input systems: variance analysis and input design issues,” Automatica, vol 42, no.410, pp. 559-572, 2006.
[16]	M, Gevers, “Identification and information matrix: how to get just sufficiently rich,” IEEE Transactions on Automatic control, vol 54, no.12, pp. 2828-2840, 2009.
[17]	Graham C Goodin, “Bias issues in closed loop identification with application to adaptive control,” Communications in Information and Systems, vol 2, no.4, pp. 349-370, 2002.
[18]	James S Welsh, “Finite sample properties of indirect nonparametric closed loop identification,” IEEE Transactions on Automatic control, vol 47, no.8, pp. 1277-1291, 2002.
[19]	Sippe G Douma, “Validity of the standard cross correlation test for model structure validation,” Automatica, vol 44, no.4, pp. 1285-1294, 2008.
[20]	Wang Jian-hong, Wang Yan-xiang. “Model structure validation for closed loop system identification,” International Journal of Modelling, Identification and Control, vol 27, no.4, 323-331, 2017.
[21]	Balazs Cs Cgaji, “Sign perturbed sums: a new system identification approach for constructing exact non-asymptotic confidence region in linear regression models,”IEEE Transactions on Signal Processing, vol 69, no.1, pp. 169-181, 2015.
[22]	Scador Kolumhan, Istran Vajk, “Perturb data sets methods for hypothesis testing and structure of corresponding confidence sets,” Automatica, vol 51, no.1, pp. 326-331, 2015.
[23]	Michel Kieffer, Eric Walter, “Guaranteed characterization of exact non-asymptotic confidence regions as defined by LSCR and SPS,” Automatica, vol 50, no.2, pp. 507-512, 2014.

Cite This Article

Plain Text BibTeX RIS

APA Style

Hong Wang-Jian, Tang De-zhi. (2017). Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Advances in Wireless Communications and Networks, 3(6), 75-83. https://doi.org/10.11648/j.awcn.20170306.11

Copy | Download

ACS Style

Hong Wang-Jian; Tang De-zhi. Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Adv. Wirel. Commun. Netw. 2017, 3(6), 75-83. doi: 10.11648/j.awcn.20170306.11

Copy | Download

AMA Style

Hong Wang-Jian, Tang De-zhi. Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Adv Wirel Commun Netw. 2017;3(6):75-83. doi: 10.11648/j.awcn.20170306.11

Copy | Download

@article{10.11648/j.awcn.20170306.11,
  author = {Hong Wang-Jian and Tang De-zhi},
  title = {Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation},
  journal = {Advances in Wireless Communications and Networks},
  volume = {3},
  number = {6},
  pages = {75-83},
  doi = {10.11648/j.awcn.20170306.11},
  url = {https://doi.org/10.11648/j.awcn.20170306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.awcn.20170306.11},
  abstract = {In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation
AU  - Hong Wang-Jian
AU  - Tang De-zhi
Y1  - 2017/12/05
PY  - 2017
N1  - https://doi.org/10.11648/j.awcn.20170306.11
DO  - 10.11648/j.awcn.20170306.11
T2  - Advances in Wireless Communications and Networks
JF  - Advances in Wireless Communications and Networks
JO  - Advances in Wireless Communications and Networks
SP  - 75
EP  - 83
PB  - Science Publishing Group
SN  - 2575-596X
UR  - https://doi.org/10.11648/j.awcn.20170306.11
AB  - In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.
VL  - 3
IS  - 6
ER  -

Copy | Download

Author Information

Hong Wang-Jian

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Hong Wang-Jian, Tang De-zhi. (2017). Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Advances in Wireless Communications and Networks, 3(6), 75-83. https://doi.org/10.11648/j.awcn.20170306.11

Copy | Download

ACS Style

Hong Wang-Jian; Tang De-zhi. Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Adv. Wirel. Commun. Netw. 2017, 3(6), 75-83. doi: 10.11648/j.awcn.20170306.11

Copy | Download

AMA Style

Hong Wang-Jian, Tang De-zhi. Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Adv Wirel Commun Netw. 2017;3(6):75-83. doi: 10.11648/j.awcn.20170306.11

Copy | Download

@article{10.11648/j.awcn.20170306.11,
  author = {Hong Wang-Jian and Tang De-zhi},
  title = {Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation},
  journal = {Advances in Wireless Communications and Networks},
  volume = {3},
  number = {6},
  pages = {75-83},
  doi = {10.11648/j.awcn.20170306.11},
  url = {https://doi.org/10.11648/j.awcn.20170306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.awcn.20170306.11},
  abstract = {In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation
AU  - Hong Wang-Jian
AU  - Tang De-zhi
Y1  - 2017/12/05
PY  - 2017
N1  - https://doi.org/10.11648/j.awcn.20170306.11
DO  - 10.11648/j.awcn.20170306.11
T2  - Advances in Wireless Communications and Networks
JF  - Advances in Wireless Communications and Networks
JO  - Advances in Wireless Communications and Networks
SP  - 75
EP  - 83
PB  - Science Publishing Group
SN  - 2575-596X
UR  - https://doi.org/10.11648/j.awcn.20170306.11
AB  - In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.
VL  - 3
IS  - 6
ER  -

Copy | Download