×

Convergence of the iterative algorithm for a general Hammerstein system identification. (English) Zbl 1218.93105

Summary: The convergence of the iterative identification algorithm for a general Hammerstein system has been an open problem for a long time. In this paper, it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters.

MSC:

93E12 Identification in stochastic control theory
93C10 Nonlinear systems in control theory
93E25 Computational methods in stochastic control (MSC2010)
Full Text: DOI

References:

[1] Bai, E. W., An optimal two stage algorithm for a class of nonlinear systems, Automatica, 34, 333-338 (1998) · Zbl 0915.93018
[2] Bai, E. W., A blind approach to the Hammerstein-Wiener model identification, Automatica, 38, 967-979 (2002) · Zbl 1012.93018
[3] Bai, E. W., Identification of linear systems with hard input nonlinearities of known structure, Automatica, 38, 853-860 (2002) · Zbl 1010.93032
[4] Bai, E. W., Frequency domain identification of Hammerstein models, IEEE Transactions on Automatic Control, 48, 530-542 (2003) · Zbl 1364.93152
[5] Bai, E. W.; Li, D., Convergence of the iterative Hammerstein system identification algorithm, IEEE Transactions on Automatic Control, 49, 1929-1940 (2004) · Zbl 1365.93098
[6] Bai, E. W.; Sastry, S. S., Persistency of excitation, sufficient richness and parameter convergence in discrete time adaptive control, Systems and Control Letters, 6, 153-163 (1985) · Zbl 0568.93043
[7] Billings, S. A.; Fakhouri, S. Y., Identification of a class of nonlinear systems using correlation analysis, Proceedings of IEE, 125, 7, 691-697 (1978)
[10] Greblicki, W., Continuous time Hammerstein system identification, IEEE Transactions on Automatic Control, 45, 1232-1236 (2000) · Zbl 0987.93019
[11] Goethals, I. K.; Pelckmans, J. Suykens; De Moor, B., Identification of MIMO Hammerstein models using least squares support vector machines, Automatica, 41, 1263-1272 (2005) · Zbl 1086.93064
[12] Liu, Y.; Bai, E. W., Recursive identification of Hammerstein systems, Automatica, 46, 346-354 (2007) · Zbl 1111.93013
[13] Narendra, K. S.; Gallman, P. G., An iterative method for the identification of nonlinear systems using a Hammerstein model, IEEE Transactions on Automatic Control, 11, 546-550 (1966)
[14] Pawlak, M., On the series expansion approach to the identification of Hammerstein systems, IEEE Transactions on Automatic Control, 36, 763-767 (1991)
[16] Stoica, P., On the convergence of an iterative algorithm used for Hammerstein system identification, IEEE Transactions on Automatic Control, 26, 967-969 (1981)
[17] Sun, L.; Liu, W.; Sano, A., Identification of dynamical system with input nonlinearity, IEE Proceedings Control Theory and Applications, 146, 1, 41-51 (1998)
[18] Voros, J., Parameter identification of discontinuous Hammerstein systems, Automatica, 33, 6, 1141-1146 (1997) · Zbl 0886.93013
[19] Westwick, D.; Verhaegen, M., Identifying MIMO Wiener systems using subspace model identification method, Signal Processing, 52, 235-258 (1996) · Zbl 0875.93093
[20] Westwick, D.; Kearney, R., Separable least squares identification of nonlinear Hammerstein models: application to stretch reflex dynamics, Annals of Biomedical Engineering, 29, 707-718 (2001)
[21] Zhao, W.; Chen, H. F., Recursive identification for Hammerstein system with ARX subsystems, IEEE Transactions on Automatic Control, 51, 1966-1974 (2006) · Zbl 1366.93689
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.