Conditional center computation in the identification of approximated Hammerstein models

The identification of Hammerstein models for nonlinear systems in considered in a worst case paradigm assuming an 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 Chebychev 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 proven. The algorithm is computational attractive in two cases: noise bounded either in l₂ or in l_∞ norm. The effectiveness of the proposed central algorithm and the comparison with the corresponding projection algorithm, which amounts to the singular value decomposition, are investigated both analytically and trough numerical examples