Discrete time Hammerstein model identification with unknown but bounded errors

In this paper the problem of Hammerstein dynamic system identification is considered when nonlinear static blocks are described by generalised polynomials and linear time invariant blocks are modelled by ARX structures. The measurement error is characterised in a set membership context. The proposed approach accomplishes parameter identification introducing an extended Hammerstein model the parameter bounds of which can derive overbounds, which can, however, be tight up against to the Hammerstein model parameter uncertainties. The procedure for deriving such overbounds is presented in detail. The consistency of the algorithm for an increasing number of measurements is theoretically proved under the standard set membership assumption that theorises no overbounding of the measurement error, the extreme values of which always reoccur. The degree of conservativeness of the overbounds is evaluated through a simulation study based on a literature model and on a large set of randomly chosen systems. Both white noise and staircase inputs are considered. The results show that in most cases the derived overbounds are at most 10% larger than the actual bounds