Improved structure selection for nonlinear models based on term clustering. (English) Zbl 0837.93009

Summary: The concepts of term clusters and cluster coefficients are defined and used in the context of system identification. It is argued that if a certain type of term in a nonlinear model is spurious, the respective cluster coefficient is small compared with the coefficients of the other clusters represented in the model. Once the spurious clusters have been detected, the corresponding terms can be deleted from the set of candidate terms. The consequences of doing this are (i) a drastic reduction in the size of the set of candidate terms and, consequently, a substantial gain in computation time is achieved; (ii) the final estimated model is more likely to reproduce the dynamics of the original system; and (iii) the final model is more robust to overparametrization. Numerical examples are included to illustrate the new procedure.


93B30 System identification
93C10 Nonlinear systems in control theory
37G99 Local and nonlocal bifurcation theory for dynamical systems
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[1] DOI: 10.1142/S0218127494000617 · Zbl 0900.70335
[2] DOI: 10.1080/00207178908953473 · Zbl 0686.93092
[3] BILLINGS . S. A. , and LEONTARITIS , I. J. , 1981 , Identification of nonliner systems using parametric estimation techniques . In IEE Conference on Control and its Applications , pp. 183 – 187 , Warwick . U.K.
[4] DOI: 10.1080/00207179008953572 · Zbl 0721.93041
[5] DOI: 10.1080/00207179108934155 · Zbl 0734.62089
[6] DOI: 10.1080/00207178608933633 · Zbl 0597.93058
[7] BLLLINGS S. A., International Journal of Control 49 pp 2157– (1989)
[8] DOI: 10.1080/00207728808964057 · Zbl 0669.93015
[9] DOI: 10.1109/82.215356 · Zbl 0825.93833
[10] ELGAR S., International Journal of Bifurcation and Chaos 3 pp p19–34– (1993) · Zbl 0875.62429
[11] DOI: 10.1142/S0218126693000046
[12] DOI: 10.1016/0167-2789(83)90112-4
[13] GUCKENHEIMER J., Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields (1983) · Zbl 0515.34001
[14] DOI: 10.1016/0005-1098(90)90044-I · Zbl 0721.93023
[15] DOI: 10.1142/S0218127493000507 · Zbl 0875.58025
[16] DOI: 10.1142/S021812749300026X · Zbl 0870.58078
[17] DOI: 10.1080/0020718508961129 · Zbl 0569.93011
[18] PARKER T. S., Practical Numerical Algorithms for Chaotic Systems (1989) · Zbl 0692.58001
[19] DOI: 10.1080/00207178908953474 · Zbl 0686.93086
[20] UEDA Y., New Approaches to Nonlinear Problems in Dynamics pp 311– (1980)
[21] WIGGINS S., Introduction to Applied Nonlinear Dynamical Systems and Chaos (1990) · Zbl 0701.58001
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