Consistency of the robust recursive Hammerstein model identification algorithm

In this paper, it is proposed a robust recursive algorithm for identification of a Hammerstein model with a static nonlinear block in polynomial form and a linear block described by ARMAX model. It is assumed that there is a priori information about a distribution class to which a disturbance belongs. Such assumption introduces a nonlinear transformation of the prediction error in the recursive algorithm. The obtained algorithm is robust in relation to the uncertainty of the disturbance distribution. By using the stochastic Lyapunov function and the martingale theory a strong consistency of estimated parameters is proved under generalized strict real positivity conditions, based on the theory of passive operators and the weakest possible excitation. The practical behavior of the robust algorithm is illustrated by simulations.