Abstract
This paper is concerned with nonparametric identification of nonlinear autoregressive systems with exogenous inputs (NARX), i.e., yk+1 = f(yk, …, yk+1-n0, uk, …, uk+1-n0)+ɛk+1. Kernel functions based stochastic approximation algorithms with expanding truncations are designed for recursively estimating the value of f(·) at any given [y(1), …,y(n0), u(1), …,u(n0)]τ ∈ R2n0. The estimates are shown to be strongly consistent. The NARX systems considered in this paper include the one in Zhao, Chen & Zheng [2008] as a special case. A numerical example is given to justify the theoretical analysis.
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