Recursive identification for hammerstein system with ARX subsystem

Identification is considered for the Hammerstein system consisting of a static nonlinear block f(*) followed by an ARX subsystem, when the system output is observed with noise. No assumption is made on the structure of f(*). Recursive estimates are given for coefficients of the ARX subsystem and for the value of f (u) at any u. All estimates are proved to converge to the true values with probability one. Numerical examples are provided justifying the theoretical analysis. Index Terms--ARX, Hammerstein system, nonparametric nonlinearity, recursive estimate, strong consistency, stochastic approximation.