Volume 2, Issue 1, March 2017, Page: 19-25
Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization
Wang Jian-hong, School of Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute, Jingdezhen, China; Dipartimento di Elettronica, Informazione Politecnico di Milano, Milano, Italy
Received: Jan. 10, 2017;       Accepted: Feb. 14, 2017;       Published: Mar. 2, 2017
DOI: 10.11648/j.mlr.20170201.13      View  1783      Downloads  85
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.
Closed Loop Identification, Tailor Made Parameterization, Recursive Algorithm, Forgetting Schemes
To cite this article
Wang Jian-hong, Recursive Algorithms of Closed Loop Identification with a Tailor Made Parameterization, Machine Learning Research. Vol. 2, No. 1, 2017, pp. 19-25. doi: 10.11648/j.mlr.20170201.13
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Edwin T, Van Donkellar, “Analysis of closed loop identification with a tailor made parameterization,” European Journal of Control, vol. 6, no. 1, pp. 54-62, 2002.
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.
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.
Mathieu Pouliquen, Olivier Gehan, “Bounded error identification for closed loop systems,” Automatica, vol. 50, no. 7, pp. 1884-1890, 2014.
Ljung, L, “System identification: Theory for the user,” Prentice Hall, 1999.
Urban Forssel, Lennart Ljung, “Closed loop identification revisted,” Automatica, vol. 35, no. 7, pp. 1215-1241, 1999.
Per Hagg, Johan Schoukens, “The transient impulse response modeling method for non-parametric system identification,” Automatica, vol. 68, no. 6, pp. 314-328, 2016.
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.
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.
G. Pillonetto, “Kernel methods in system identification, machine learning and function estimation: a survey,” Automatica., vol. 50, pp. 657–682, Mar. 2013.
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.
Browse journals by subject