NONPARAMETRIC APPROACH TO IDENTIFYING NARX SYSTEMS

Qijiang SONG;Han-Fu CHEN

Journal of Systems Science & Complexity ›› 2010, Vol. 23 ›› Issue (1) : 3-021.

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Journal of Systems Science & Complexity ›› 2010, Vol. 23 ›› Issue (1) : 3-021. DOI: 10.1007/s11424-010-9268-1
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NONPARAMETRIC APPROACH TO IDENTIFYING NARX SYSTEMS

  • Qijiang SONG, Han-Fu CHEN
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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.

Key words

a-mixing / geometrically ergodic / Markov chains / NARX / nonparametric / recursive estimate / stochastic approximation / strongly consistent.

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Qijiang SONG , Han-Fu CHEN. NONPARAMETRIC APPROACH TO IDENTIFYING NARX SYSTEMS. Journal of Systems Science and Complexity, 2010, 23(1): 3-021 https://doi.org/10.1007/s11424-010-9268-1
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