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A novel two-stage estimation algorithm for nonlinear Hammerstein-Wiener systems from noisy input and output data. (English) Zbl 1378.93131
Summary: This paper investigates the identification problem of Hammerstein-Wiener errors-in-variable systems where the measurement errors of the system input and output are either temporally white or have relatively short memory size compared to the data length, but the corresponding variances are unknown. A two-stage algorithm is developed to estimate the unknown parameters with the first stage employing a modified bias-eliminating least squares algorithm, followed by a singular value decomposition in the second stage. Our proposed estimator is shown to be asymptotically unbiased. The simulation result shows the effectiveness of the proposed algorithm.

MSC:
93E12 Identification in stochastic control theory
93E10 Estimation and detection in stochastic control theory
93C10 Nonlinear systems in control theory
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[1] Ding, F., System identification-new theory and methods, (2013), Science Press Beijing
[2] Ding, F., System identification-performances analysis for identification methods, (2014), Science Press Beijing
[3] Shi, Y.; Chen, T. W., Optimal design of multichannel transmultiplexers with stopband energy and passband magnitude constraints, IEEE Trans. Circuits Syst. II—Analog Digit. Signal Process., 50, 9, 659-662, (2003)
[4] Liu, D.; Yang, Y.; Zhang, Y., Robust fault estimation for singularly perturbed systems with Lipschitz nonlinearity, J. Frankl. Inst., 353, 4, 876-890, (2016) · Zbl 1395.93196
[5] Du, T.; Guo, L., Unbiased information filtering for systems with missing measurement based on disturbance estimation, J. Frankl. Inst., 353, 4, 936-954, (2016) · Zbl 1395.93533
[6] Wang, X. H.; Ding, F., Convergence of the auxiliary model-based multi-innovation generalized extended stochastic gradient algorithm for box-Jenkins systems, Nonlinear Dyn., 82, 1-2, 269-280, (2015) · Zbl 1348.93086
[7] Xiong, W. L.; Yang, X. Q.; Ke, L.; Xu, B. G., EM algorithm-based identification of a class of nonlinear Wiener systems with missing output data, Nonlinear Dyn., 80, 1-2, 329-339, (2015) · Zbl 1345.93151
[8] Zhang, Y.; Zhao, Z.; Cui, G. M., Auxiliary model method for transfer function estimation from noisy input and output data, Appl. Math. Model., 39, 15, 4257-4265, (2015)
[9] Söderström, T., Comparing some classes of bias-compensating least squares methods, Automatica, 49, 3, 840-845, (2013) · Zbl 1267.93176
[10] Ljung, L., System identification—theory for the user, (1999), Prentice Hall Upper Saddle River, NJ, USA
[11] Huffel, S., Recent advances in total least squares techniques and errors-in-variables modeling, (1997), SIAM Philadelphia, PA · Zbl 0861.00018
[12] Huffel, S.; Lemmerling, P., Total least squares and errors-in-variables modeling. analysis, algorithms and applications, (2002), Kluwer Dordrecht, The Netherlands · Zbl 0984.00011
[13] Mu, B.; Chen, H., Recursive identification of errors-in-variables Wiener systems, Automatica, 49, 9, 2744-2753, (2013) · Zbl 1364.93832
[14] Söderström, T.; Irshad, Y.; Mossberg, M.; Zheng, W., On the accuracy of a covariance matching method for continuous-time errors-in-variables identification, Automatica, 49, 10, 2982-2993, (2013) · Zbl 1358.93177
[15] Song, Q., Identification of errors-in-variables systems with nonlinear output observations, Automatica, 49, 4, 987-992, (2013) · Zbl 1284.93245
[16] Söderström, T., Errors-in-variables methods in system identification, Automatica, 43, 6, 939-958, (2007) · Zbl 1193.93090
[17] Söderström, T.; Mossberg, M.; Hong, M., A covariance matching approach for identifying errors-in-variables systems, Automatica, 45, 9, 2018-2031, (2009) · Zbl 1175.93231
[18] Bai, E., An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems, Automatica, 34, 3, 333-338, (1998) · Zbl 0915.93018
[19] Liu, X. G.; Zhou, Y. X.; Cong, L.; Ding, F., High-purity control of internal thermally coupled distillation columns based on the nonlinear wave model, J. Process Control, 21, 6, 920-926, (2011)
[20] Chen, J.; Lv, L. X.; Ding, R. F., Multi-innovation stochastic gradient algorithms for dual-rate sampled systems with preload nonlinearity, Appl. Math. Lett., 26, 1, 124-129, (2013) · Zbl 1251.93130
[21] Malekshahi, E.; Mohammadi, S. M.A., The model order reduction using LS, RLS and MV estimation methods, Int. J. Control Autom. Syst., 12, 3, 572-581, (2014)
[22] Wang, D. Q.; Shan, T.; Ding, R., Data filtering based stochastic gradient algorithms for multivariable CARAR-like systems, Math. Model. Anal., 18, 3, 374-385, (2013) · Zbl 1271.93164
[23] Wang, D. Q.; Ding, F.; Liu, X. M., Least squares algorithm for an input nonlinear system with a dynamic subspace state space model, Nonlinear Dyn., 75, 1-2, 49-61, (2014) · Zbl 1281.93050
[24] Wang, Z. Y.; Shen, Y. X.; Wu, D. H.; Ji, Z. C., Hierarchical least squares algorithms for nonlinear feedback system modeling, J. Frankl. Inst., 353, 10, 2258-2269, (2016) · Zbl 1347.93275
[25] Ase, H.; Katayama, T., A subspace-based identification of Wiener-Hammerstein benchmark model, Control Eng. Pract., 44, 126-137, (2015)
[26] Mu, B. Q.; Chen, H. F., Recursive identification of errors-in-variables Wiener-Hammerstein systems, Eur. J. Control, 20, 1, 14-23, (2014) · Zbl 1293.93755
[27] Schoukens, M.; Marconato, A.; Pintelon, R.; Vandersteen, G.; Rolain, Y., Parametric identification of parallel Wiener-Hammerstein systems, Automatica, 51, 111-122, (2015) · Zbl 1309.93174
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