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
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