Convergence analysis for recursive Hammerstein identification

This paper derives a recursive prediction error identification method based on the Hammerstein model structure. The convergence properties of the algorithm are analysed by application of Ljung’s associated differential equation method. It is proved that the algorithm can only converge to stable stationary points of the associated ordinary differential equation. General conditions for local convergence to the true parameter vector are given, and the cases with piecewise linear and polynomial nonlinearities are treated in detail. The derived identification method is illustrated in a numerical study that treats identification of a subsystem of a cement mill.