Pathwise convergence of recursive identification algorithms for Hammerstein systems

This paper gives estimates for: 1) coefficients contained in the linear part of the Hammerstein system; 2) the value of the nonlinear function f(u) in the Hammerstein system at any u; 3) Ef(u_k) and Eu_kf(u_k) with u_k denoting the system input. No assumption is made on structure of f(·). The estimates given by the stochastic approximation algorithms with expanding truncations are recursive and convergent to the true values with probability one. Two numerical examples are given.