Least squares based and gradient based iterative identification for Wiener nonlinear systems. (English) Zbl 1219.94052

Summary: This paper derives a least squares-based and a gradient-based iterative identification algorithms for Wiener nonlinear systems. These methods separate one bilinear cost function into two linear cost functions, estimating directly the parameters of Wiener systems without re-parameterization to generate redundant estimates. The simulation results confirm that the proposed two algorithms are valid and the least squares-based iterative algorithm has faster convergence rates than the gradient-based iterative algorithm.


94A12 Signal theory (characterization, reconstruction, filtering, etc.)
93B30 System identification
Full Text: DOI


[1] Ding, F.; Chen, T.: Identification of Hammerstein nonlinear ARMAX systems, Automatica 41, No. 9, 1479-1489 (2005) · Zbl 1086.93063
[2] Ding, F.; Shi, Y.; Chen, T.: Auxiliary model based least-squares identification methods for Hammerstein output-error systems, Systems control letters 56, No. 5, 373-380 (2007) · Zbl 1130.93055
[3] Umoh, I. J.; Ogunfunmi, T.: An affine projection-based algorithm for identification of nonlinear Hammerstein systems, Signal processing 90, No. 6, 2020-2030 (2010) · Zbl 1197.94133
[4] Wang, D. Q.; Chu, Y. Y.; Ding, F.: Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA systems, Computers mathematics with applications 59, No. 9, 3092-3098 (2010) · Zbl 1193.93170
[5] Wang, D. Q.; Chu, Y. Y.; Yang, G. W.; Ding, F.: Auxiliary model-based recursive generalized least squares parameter estimation for Hammerstein OEAR systems, Mathematical and computer modelling 52, No. 1–2, 309-317 (2010) · Zbl 1201.93134
[6] Vörös, J.: Modeling and identification of Wiener systems with two-segment nonlinearities, IEEE transactions on control systems technology 11, No. 2, 253-257 (2003)
[7] Vörös, J.: Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities, Systems control letters 56, No. 2, 99-105 (2007) · Zbl 1112.93019
[8] Aguirre, L. A.; Coelho, M. C. S.; Corrêa, M. V.: On the interpretation and practice of dynamical difference between Hammerstein and Wiener models, IEE prooceedings of control theory and applications 152, No. 4, 349-356 (2005)
[9] Hu, X. L.; Chen, H. F.: Strong consistence of recursive identification for Wiener systems, Automatica 41, No. 11, 1905-1916 (2005) · Zbl 1087.93057
[10] Kozek, M.; Sinanović, S.: Identification of Wiener models using optimal local linear models, Simulation modelling practice and theory 16, No. 8, 1055-1066 (2008)
[11] Figueroa, J. L.; Biagiola, S. I.; Agamennoni, O. E.: An approach for identification of uncertain Wiener systems, Mathematical and computer modelling 48, No. 1–2, 305-315 (2008) · Zbl 1145.93432
[12] Hagenblad, A.; Ljung, L.; Wills, A.: Maximum likelihood identification of Wiener models, Automatica 44, No. 11, 2697-2705 (2008) · Zbl 1152.93508
[13] Ding, F.; Liu, P. X.; Liu, G.: Gradient based and least-squares based iterative identification methods for OE and OEMA systems, Digital signal processing 20, No. 3, 664-677 (2010)
[14] Liu, Y. J.; Wang, D. Q.; Ding, F.: Least-squares based iterative algorithms for identifying box-Jenkins models with finite measurement data, Digital signal processing 20, No. 5, 1458-1467 (2010)
[15] Wang, D. Q.; Yang, G. W.; Ding, R. F.: Gradient-based iterative parameter estimation for box-Jenkins systems, Computers mathematics with applications 60, No. 5, 1200-1208 (2010) · Zbl 1201.94046
[16] Kapetanios, G.: A note on an iterative least-squares estimation method for ARMA and VARMA models, Economics letters 79, No. 3, 305-312 (2003) · Zbl 1255.62254
[17] Bai, E. W.; Liu, Y.: Least squares solutions of bilinear equations, Systems control letters 55, No. 6, 466-472 (2006) · Zbl 1129.65310
[18] Ding, F.; Chen, T.: Hierarchical gradient-based identification of multivariable discrete-time systems, Automatica 41, No. 2, 315-325 (2005) · Zbl 1073.93012
[19] Ding, F.; Chen, T.: Hierarchical least squares identification methods for multivariable systems, IEEE transactions on automatic control 50, No. 3, 397-402 (2005) · Zbl 1365.93551
[20] Ding, F.; Chen, T.: Hierarchical identification of lifted state-space models for general dual-rate systems, IEEE transactions on circuits and systems–I: regular papers 52, No. 6, 1179-1187 (2005) · Zbl 1374.93342
[21] D.Q. Wang, Y.Y. Chu, F. Ding, Identification methods for Wiener nonlinear systems based on the least squares and gradient iterations, in: 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, December 16–18, 2009, Shanghai, China, pp. 3632–3636.
[22] Ding, F.; Chen, T.: Performance analysis of multi-innovation gradient type identification methods, Automatica 43, No. 1, 1-14 (2007) · Zbl 1140.93488
[23] Ding, F.: Several multi-innovation identification methods, Digital signal processing 20, No. 4, 1027-1039 (2010)
[24] Wang, D. Q.; Ding, F.: Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems, Digital signal processing 20, No. 3, 750-762 (2010)
[25] Ding, F.; Liu, P. X.; Liu, G.: Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises, Signal processing 89, No. 10, 1883-1890 (2009) · Zbl 1178.94137
[26] Han, L. L.; Ding, F.: Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital signal processing 19, No. 4, 545-554 (2009)
[27] Zhang, J. B.; Ding, F.; Shi, Y.: Self-tuning control based on multi-innovation stochastic gradient parameter estimation, Systems control letters 58, No. 1, 69-75 (2009) · Zbl 1154.93040
[28] Ding, F.; Liu, P. X.; Liu, G.: Multi-innovation least squares identification for linear and pseudo-linear regression models, IEEE transactions on systems, man, and cybernetics, part B: cybernetics 40, No. 3, 767-778 (2010)
[29] Xie, L.; Liu, Y. J.; Yang, H. Z.; Ding, F.: Modeling and identification for non-uniformly periodically sampled-data systems, IET control theory applications 4, No. 5, 784-794 (2010)
[30] Bai, E. W.: An optimal two-stage identification algorithm for Hammerstein–Wiener nonlinear systems, Automatica 34, No. 3, 333-338 (1998) · Zbl 0915.93018
[31] Wang, D. Q.; Ding, F.: Extended stochastic gradient identification algorithms for Hammerstein–Wiener ARMXA systems, Computers and mathematics with applications 56, No. 12, 3157-3164 (2008) · Zbl 1165.65308
[32] Liu, Y.; Bai, E. W.: Iterative identification of Hammerstein systems, Automatica 43, No. 2, 346-354 (2007) · Zbl 1111.93013
[33] Cerone, V.; Regruto, D.: Parameter bounds for discrete-time Hammerstein models with bounded output errors, IEEE transactions on automatic control 48, No. 10, 1855-1860 (2003) · Zbl 1364.93417
[34] Ding, F.; Ding, J.: Least squares parameter estimation with irregularly missing data, International journal of adaptive control and signal processing 24, No. 7, 540-553 (2010) · Zbl 1200.93130
[35] Ding, F.; Qiu, L.; Chen, T.: Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems, Automatica 45, No. 2, 324-332 (2009) · Zbl 1158.93365
[36] Ding, F.; Liu, G.; Liu, X. P.: Partially coupled stochastic gradient identification methods for non-uniformly sampled systems, IEEE transaction on automatic control 55, No. 8, 1976-1981 (2010) · Zbl 1368.93121
[37] Liu, Y. J.; Xie, L.; Ding, F.: An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems, Proceedings of the institution of mechanical engineers, part I: Journal of systems and control engineering 223, No. 4, 445-454 (2009)
[38] Ding, F.; Liu, P. X.; Yang, H. Z.: Parameter identification and intersample output estimation for dual-rate systems, IEEE transactions on systems, man, and cybernetics, part A: systems and humans 38, No. 4, 966-975 (2008)
[39] Ding, J.; Shi, Y.; Wang, H. G.; Ding, F.: A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems, Digital signal processing 20, No. 4, 1238-1249 (2010)
[40] Wang, D. Q.; Ding, F.: Input–output data filtering based recursive least squares identification for CARARMA systems, Digital signal processing 20, No. 4, 991-999 (2010)
[41] F. Ding, P.X. Liu, G. Liu, Identification methods for Hammerstein nonlinear systems, Digital Signal Processing 21 (2) (2011), doi:10.1016/j.dsp.2010.06.006
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.