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Nonparametric approach to identifying NARX systems

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Abstract

This paper considers identification of the nonlinear autoregression with exogenous inputs (NARX system). The growth rate of the nonlinear function is required be not faster than linear with slope less than one. The value of f(·) at any fixed point is recursively estimated by the stochastic approximation (SA) algorithm with the help of kernel functions. Strong consistency of the estimates is established under reasonable conditions, which, in particular, imply stability of the system. The numerical simulation is consistent with the theoretical analysis.

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Qijiang Song & Han-Fu Chen

Authors
  1. Qijiang Song
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  2. Han-Fu Chen
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Correspondence to Qijiang Song.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 60821091 and 60874001, by a Grant from the National Laboratory of Space Intelligent Control, and by the Guozhi Xu Posdoctoral Research Foundation.

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Song, Q., Chen, HF. Nonparametric approach to identifying NARX systems. J Syst Sci Complex 23, 3–21 (2010). https://doi.org/10.1007/s11424-010-9268-1

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  • DOI: https://doi.org/10.1007/s11424-010-9268-1

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