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Identification of nonlinear characteristics of a class of block-oriented nonlinear systems via Daubechies wavelet-based models. (English) Zbl 1060.93034

This paper deals with the problem of identification of nonlinear characteristics of a class of block-oriented dynamical systems where prior knowledge about subsystems is non-parametric, excluding implementation of standard parametric identification methods. A class of Daubechies wavelet-based models using only input-output measurement data is introduced and their accuracy is investigated in the global MISE error sense. The convergence of the proposed models is proved provided that the model complexity is appropriately fitted to the number of measurements. Simulation examples are given for illustrating the theory.

MSC:

93B30 System identification
93C10 Nonlinear systems in control theory
65T60 Numerical methods for wavelets
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[1] BENDAT J. S., Nonlinear System Analysis and Identification (1990) · Zbl 0715.93063
[2] DOI: 10.1109/49.192728 · doi:10.1109/49.192728
[3] BILLINGS S. A., Proceedings of the IEE. 127 pp 272– (1980)
[4] DOI: 10.1016/0005-1098(82)90022-X · Zbl 0472.93067 · doi:10.1016/0005-1098(82)90022-X
[5] DOI: 10.1214/aos/1018031262 · Zbl 0954.62047 · doi:10.1214/aos/1018031262
[6] DOI: 10.1109/18.335971 · Zbl 0819.94005 · doi:10.1109/18.335971
[7] DOI: 10.1109/5.362753 · doi:10.1109/5.362753
[8] DAUBECHIES I., Ten Lectures on Wavelets (1992) · Zbl 0776.42018
[9] DELYON B., Wavelets and Statistics pp 151– (1995) · doi:10.1007/978-1-4612-2544-7_10
[10] DOI: 10.1007/978-1-4471-0107-9 · doi:10.1007/978-1-4471-0107-9
[11] ESKINAT E., American Institute of Chemical Engineering 37 pp 255– (1991) · doi:10.1002/aic.690370211
[12] DOI: 10.1016/0098-1354(96)00176-7 · doi:10.1016/0098-1354(96)00176-7
[13] DOI: 10.1016/S0165-1684(00)00231-0 · Zbl 1079.93500 · doi:10.1016/S0165-1684(00)00231-0
[14] DOI: 10.1109/78.134443 · Zbl 0760.93082 · doi:10.1109/78.134443
[15] DOI: 10.1080/00207728908910318 · Zbl 0688.93062 · doi:10.1080/00207728908910318
[16] DOI: 10.1109/18.149500 · Zbl 0767.93012 · doi:10.1109/18.149500
[17] DOI: 10.1109/TAC.1986.1104096 · Zbl 0584.93066 · doi:10.1109/TAC.1986.1104096
[18] DOI: 10.1109/9.328819 · Zbl 0824.93068 · doi:10.1109/9.328819
[19] DOI: 10.1080/00207727908941660 · Zbl 0416.93017 · doi:10.1080/00207727908941660
[20] DOI: 10.1007/BF02481112 · Zbl 0623.62029 · doi:10.1007/BF02481112
[21] DOI: 10.1080/00207178708933731 · Zbl 0613.93062 · doi:10.1080/00207178708933731
[22] DOI: 10.1016/0165-1684(91)90029-I · Zbl 0725.93028 · doi:10.1016/0165-1684(91)90029-I
[23] DOI: 10.1080/00207729408928949 · Zbl 0790.93033 · doi:10.1080/00207729408928949
[24] GREBLICKI W., Control-Theory and Advanced Technology 10 pp 771– (1994)
[25] DOI: 10.1109/18.333862 · Zbl 0813.93067 · doi:10.1109/18.333862
[26] HABER R., Nonlinear System Identification: Input-Output Modeling Approach (1999) · Zbl 0934.93004 · doi:10.1007/978-94-011-4481-0
[27] HANNAN E. J., The Statistical Theory of Linear Systems (1988) · Zbl 0641.93002
[28] HÄRDLE W., Wavelets. Approximation, and Statistical Applications (1998) · Zbl 0899.62002 · doi:10.1007/978-1-4612-2222-4
[29] DOI: 10.1080/00207728708963996 · Zbl 0623.93017 · doi:10.1080/00207728708963996
[30] DOI: 10.1080/00207728808967621 · Zbl 0658.93064 · doi:10.1080/00207728808967621
[31] DOI: 10.1080/00207728808964072 · Zbl 0659.93017 · doi:10.1080/00207728808964072
[32] DOI: 10.1080/00207728908910324 · Zbl 0686.93087 · doi:10.1080/00207728908910324
[33] DOI: 10.1002/(SICI)1099-1115(199912)13:8<691::AID-ACS591>3.0.CO;2-7 · Zbl 0953.93021 · doi:10.1002/(SICI)1099-1115(199912)13:8<691::AID-ACS591>3.0.CO;2-7
[34] DOI: 10.1016/S0165-1684(00)00247-4 · Zbl 1098.94545 · doi:10.1016/S0165-1684(00)00247-4
[35] HUNTER I. W., Biological Cybernetics pp 135– (1986)
[36] JANG W., Journal of Audio Engineering Society 42 pp 50– (1994)
[37] DOI: 10.1007/978-1-4613-0145-5 · Zbl 0989.94001 · doi:10.1007/978-1-4613-0145-5
[38] DOI: 10.1016/0005-1098(95)00119-1 · Zbl 0846.93019 · doi:10.1016/0005-1098(95)00119-1
[39] DOI: 10.1061/(ASCE)0733-9399(1998)124:10(1059) · doi:10.1061/(ASCE)0733-9399(1998)124:10(1059)
[40] DOI: 10.1080/00207728908910255 · Zbl 0687.93075 · doi:10.1080/00207728908910255
[41] KWAK, B. J., YAGLE, A. E. and LEVITT, J. A. Non-linear system identification of hydraulic actuator. Friction dynamics using a Hammerstein model. Proceedings IEEE International Conference on Acoustics. Speech and Signal Processing ICASSP’98. Vol. 4, pp.1933–1936.
[42] MALLAT S. G., A Wavelet Tour of Signal Processing (1998) · Zbl 1125.94306
[43] DOI: 10.1109/TBME.1974.324293 · doi:10.1109/TBME.1974.324293
[44] DOI: 10.1109/9.86954 · doi:10.1109/9.86954
[45] DOI: 10.1109/81.721260 · Zbl 0952.93021 · doi:10.1109/81.721260
[46] DOI: 10.1016/0167-7152(87)90044-7 · Zbl 0605.62030 · doi:10.1016/0167-7152(87)90044-7
[47] SCOTT D. W., Mulfivariate Density Estimation. Theory. Practice, and Visualization (1992) · doi:10.1002/9780470316849
[48] DOI: 10.1016/0005-1098(95)00120-8 · Zbl 0846.93018 · doi:10.1016/0005-1098(95)00120-8
[49] DOI: 10.1214/aos/1176345969 · Zbl 0511.62048 · doi:10.1214/aos/1176345969
[50] DOI: 10.1109/9.746278 · Zbl 1056.93519 · doi:10.1109/9.746278
[51] SLIWINSKI P., Non-linear system identification using wavelet algorithms (2000)
[52] DOI: 10.1109/9.802933 · Zbl 1136.93446 · doi:10.1109/9.802933
[53] WALLEN A., Tools for Autonomous Process Control (2000)
[54] DOI: 10.1049/ip-cta:20010238 · doi:10.1049/ip-cta:20010238
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