Recursive Identification for Hammerstein System With ARX Subsystem

Identification is considered for the Hammerstein system consisting of a static nonlinear block f(middot) followed by an ARX subsystem, when the system output is observed with noise. No assumption is made on the structure of f(middot). 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