Identification of approximated Hammerstein models in a worst-case setting

The identification of Hammerstein models for nonlinear systems in considered in a worst-case setting, assuming unknown-but-bounded measurement noise. A new approach is proposed in which the identification of a low-complexity Hammerstein model amounts to the computation of the Chebichev center of a set of matrices conditioned to the manifold of rank-one matrices. An identification algorithm, based on a relaxation technique, is proposed and its consistency is proven. The algorithm is computationally attractive in two cases: noise bounded either in l2 or in l-infinity norm. The effectiveness of the proposed central algorithm and the comparison with the corresponding projection algorithm, which is based on the singular-value decomposition, are investigated both analytically and through numerical examples. In particular, tight error bounds are obtained for the projection algorithm.