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(k)f(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.