The Hammerstein–Wiener Model for Identification of Stochastic Systems

Identification of nonlinear stochastic systems in the class of Hammerstein–Wiener models is studied. The problem is specific due to the nonlinearities of the investigated object. Hammerstein–Wiener models are constructed with regard for the disturbances of the type of white noise and martingale sequence at the output of the object. A two-stage recursive identification algorithm is designed. Necessary and sufficient conditions for the strong consistency of parameter estimates found by this algorithm are formulated. The results are applied to adaptive tracking of the output of an object.