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.sub.k]) and E[u.sub.k]f([u.sub.k]) with [u.sub.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. Index Terms--Hammerstein system, nonparametric nonlinearity, recursive estimate, stochastic approximation, strong consistency.