Computational burden reduction in set-membership identification of Wiener models

Recent results on set-membership identification presented in the literature show that the computation of parameter bounds requires the solution to a set of polynomial optimization problems. Although, in principle, global optimal solutions to such problems can be computed by applying suitable convex relaxation techniques, based on sum-of-squares decomposition and/or generalized moment theory, practical applicability of such methods are limited in practice by the high computational complexity. In this paper, we propose an original approach for reducing the computational load of the relaxed problems in terms of a reduction of the number of optimization variables. We also give a numerical example to show the effectiveness of the proposed technique.