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Recursive Identification of Hammerstein Systems with Polynomial Function Approximation
International Journal of Management and Fuzzy Systems
Volume 3, Issue 6, December 2017, Pages: 87-94
Received: Sep. 25, 2017; Accepted: Oct. 27, 2017; Published: Nov. 20, 2017
Authors
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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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.
Keywords
Nonlinear System, Hammerstein Systems, Polynomial Functions Approximation, Recursive Identification, Singular Value Decomposition
Wang Jian-hong, Tang De-zhi, Jiang Hong, Tang Xiao-jun, Recursive Identification of Hammerstein Systems with Polynomial Function Approximation, International Journal of Management and Fuzzy Systems. Vol. 3, No. 6, 2017, pp. 87-94. doi: 10.11648/j.ijmfs.20170306.12
References
[1]
Anna Hagenblad, Lennart Ljung, Adrian Wills. Maximum likelihood identification of Wiener models[J]. Automatica, 2008.44(11):2697-2705.
[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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