Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. (English) Zbl 1165.65308

Summary: An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein-Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identification model include the product terms of the parameters of the original systems. Two methods of separating the parameter estimates of the original parameters from the product terms are discussed: the average method and the singular value decomposition method. To improve the identification accuracy, an extended stochastic gradient algorithm with a forgetting factor is presented. The simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor.


65C30 Numerical solutions to stochastic differential and integral equations
93E10 Estimation and detection in stochastic control theory
62F10 Point estimation
62H12 Estimation in multivariate analysis
Full Text: DOI


[1] D.Q. Wang, F. Ding, Gradient based estimation methods for a class of nonlinear systems with colored noises, in: Proceedings of 2008 IEEE International Conference on Automation and Logistics, ICAL 2008, September 1-3, 2008, Qingdao, China, pp. 736-739
[2] Ding, F.; Chen, T., Identification of Hammerstein nonlinear ARMAX systems, Automatica, 41, 9, 1479-1489, (2005) · Zbl 1086.93063
[3] Ding, F.; Shi, Y.; Chen, T., Auxiliary model based least-squares identification methods for Hammerstein output-error systems, Systems & control letters, 56, 5, 373-380, (2007) · Zbl 1130.93055
[4] Ding, F.; Shi, Y.; Chen, T., Gradient-based identification methods for Hammerstein nonlinear ARMAX models, Nonlinear dynamics, 45, 1-2, 31-43, (2006) · Zbl 1134.93321
[5] Ding, F.; Chen, T.; Iwai, Z., Adaptive digital control of Hammerstein nonlinear systems with limited output sampling, SIAM journal on control and optimization, 45, 6, 2257-2276, (2007) · Zbl 1126.93034
[6] Chaoui, F.Z.; Giri, F.; Rochdi, Y.; Haloua, M.; Naitali, A., System identification based on Hammerstein model, International journal of control, 78, 6, 430-442, (2005) · Zbl 1134.93411
[7] Vörös, J., An iterative method for wiener – hammerstein systems parameter identification, Journal of electrical engineering, 58, 2, 114-117, (2007)
[8] Bai, E.W., Decoupling the linear and nonlinear parts in Hammerstein model identification, Automatica, 40, 4, 671-676, (2004) · Zbl 1168.93328
[9] Sung, S.W.; Lee, J., Modeling and control of Wiener-type processes, Chemical engineering science, 59, 7, 1515-1521, (2004)
[10] Moustafa, K.A.F.; Emara-shabaik, H.E., Recursive parameter identification of a class of nonlinear systems from noisy measurements, Journal of vibration and control, 6, 1, 49-60, (2000) · Zbl 1071.93512
[11] Emara-shabaik, H.E.; Ahmed, M.S.; Al-ajmi, K.H., Wiener – hammerstein model identification-recursive algorithms, JSME international journal series C, 45, 2, 606-613, (2002)
[12] Zhu, Y.C., Estimation of an N-L-N hammerstein – wiener model, Automatica, 38, 9, 1607-1614, (2002) · Zbl 1012.93019
[13] Bolkvadze, G.R., The hammerstein – wiener model for identification of stochastic systems, Automation and remote control, 64, 9, 1418-1431, (2003) · Zbl 1078.93068
[14] Vörös, J., An iterative method for hammerstein – wiener systems parameter identification, Journal of electrical engineering, 55, 11-12, 328-331, (2004)
[15] Bai, E.W., An optimal two-stage identification algorithm for hammerstein – wiener nonlinear systems, Automatica, 34, 3, 333-338, (1998) · Zbl 0915.93018
[16] Bai, E.W., A blind approach to the hammerstein – wiener model identification, Automatica, 38, 6, 967-979, (2002) · Zbl 1012.93018
[17] Goodwin, G.C.; Sin, K.S., Adaptive filtering prediction and control, (1984), Prentice-hall Englewood Cliffs, NJ · Zbl 0653.93001
[18] Wei, F.; Ding, F., Three methods of separating parameters for Hammerstein nonlinear systems, Science technology and engineering, 8, 6, 1586-1589, (2008)
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