New bound characteristics of NARX model in the frequency domain
Jing, X.J., Lang, Z.Q. and Billings, S.A.
(2006)
New bound characteristics of NARX model in the frequency domain.
Research Report.
ACSE Research Report no. 937
.
Automatic Control and Systems Engineering, University of Sheffield
Abstract
New results about the bound characteristics of both the generalized frequency response functions (GFRFs) and the output frequency response for the NARX (Nonlinear AutoRegressive model with eXogenous input) model are established. It is shown that the magnitudes of the GFRFs and the system output spectrum can all be bounded by a polynomial function of the magnitude bound of the first order GFRF, and the coefficients of the polynomial are functions of the NARX model parameters. These new bound characteristics of the NARX model provide an important insight into the relationship between the model parameters and the magnitudes of the system frequency response functions, reveal the effect of the model parameters on the stability of the NARX model to a certain extent, and provide a useful technique to evaluate the truncation error in a Volterra series expression of nonlinear systems, and the highest order needed in the Volterra series approximation. A numerical example is given to demonstrate the effectiveness of the theoretical results.
Metadata
Item Type:
Monograph
Authors/Creators:
Jing, X.J.
Lang, Z.Q.
Billings, S.A.
Copyright, Publisher and Additional Information:
The Department of Automatic Control and Systems Engineering research reports offer a forum for the research output of the academic staff and research students of the Department at the University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. Some papers in the series may have been subsequently published elsewhere and you are advised to cite the later published version in these instances.
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