Identification of IIR Wiener systems with spline nonlinearities that have variable knots
An algorithm is developed for the identification of Wiener systems, linear dynamic elements followed by static nonlinearities. In this case, the linear element is modeled using a recursive digital filter, while the static nonlinearity is represented by a spline of arbitrary but fixed degree. The pri...
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Published in | IEEE transactions on automatic control Vol. 50; no. 10; pp. 1617 - 1622 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York
IEEE
01.10.2005
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subjects | |
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Abstract | An algorithm is developed for the identification of Wiener systems, linear dynamic elements followed by static nonlinearities. In this case, the linear element is modeled using a recursive digital filter, while the static nonlinearity is represented by a spline of arbitrary but fixed degree. The primary contribution in this note is the use of variable knot splines, which allow for the use of splines with relatively few knot points, in the context of Wiener system identification. The model output is shown to be nonlinear in the filter parameters and in the knot points, but linear in the remaining spline parameters. Thus, a separable least squares algorithm is used to estimate the model parameters. Monte-Carlo simulations are used to compare the performance of the algorithm identifying models with linear and cubic spline nonlinearities, with a similar technique using polynomial nonlinearities. |
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AbstractList | An algorithm is developed for the identification of Wiener systems, linear dynamic elements followed by static nonlinearities. In this case, the linear element is modeled using a recursive digital filter, while the static nonlinearity is represented by a spline of arbitrary but fixed degree. The primary contribution in this note is the use of variable knot splines, which allow for the use of splines with relatively few knot points, in the context of Wiener system identification. The model output is shown to be nonlinear in the filter parameters and in the knot points, but linear in the remaining spline parameters. Thus, a separable least squares algorithm is used to estimate the model parameters. Monte-Carlo simulations are used to compare the performance of the algorithm identifying models with linear and cubic spline nonlinearities, with a similar technique using polynomial nonlinearities. |
Author | Hughes, M.C. Westwick, D.T. |
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CitedBy_id | crossref_primary_10_1109_TSP_2012_2190404 crossref_primary_10_1016_j_phpro_2012_05_126 crossref_primary_10_1080_00207721_2012_669863 crossref_primary_10_1049_iet_cta_2012_0548 crossref_primary_10_3182_20130703_3_FR_4038_00065 crossref_primary_10_1016_j_ifacol_2016_07_334 crossref_primary_10_1016_j_ifacol_2021_08_437 crossref_primary_10_1080_00207721_2016_1244303 |
Cites_doi | 10.1109/19.982982 10.1137/0710036 10.1109/81.586027 10.1007/BF01732610 10.1109/ACC.2002.1023129 10.1016/0005-1098(92)90037-G 10.1016/S0005-1098(03)00149-3 10.1109/ACC.1999.782408 10.1114/1.232 10.1016/0165-1684(96)00056-4 10.1016/S0959-1524(00)00056-1 10.1016/S0005-1098(01)00292-8 10.1109/9.333765 10.1109/TBME.2003.820384 10.1016/S0947-3580(99)70146-9 10.1016/0165-1684(96)00067-9 10.1109/26.764925 10.1002/0471722960 10.1016/0005-1098(93)90103-Z |
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References | ref12 ref14 crama (ref13) 2003; 13 ref11 ref2 ref1 ref17 ref16 ref19 ref18 lancaster (ref23) 1986 sjöberg sjoberg (ref24) 1997; 7 wigren (ref25) 2003 ref21 bai (ref6) 2003; 39 abd-elrady (ref20) 2002; 15 ref8 ljung (ref22) 1999 ref7 wigren (ref10) 1993; 29 ref9 ref4 ref3 ref5 bai (ref15) 2002; 38 |
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SubjectTerms | Adaptive control Automatic control Block structured models Computer simulation Control systems cubic spline Levenberg-Marquardt algorithm Multidimensional systems nonlinear system identification Piecewise linear techniques Recursive estimation separable least squares optimization Spline Stochastic processes Upper bound |
Title | Identification of IIR Wiener systems with spline nonlinearities that have variable knots |
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