Bounding nonconvex feasible sets in set membership identification: OE and ARX models with quantized information

Set membership system identification is based on the assumption that the uncertainties affecting the data or the model are unknown-but-bounded. When dealing with parametric models, the problem boils down to estimate the feasible parameter set, which is the set of all parameter values that are compatible with the available information. Unfortunately, feasible sets turn out to be nonconvex in several settings, including OE models with bounded output noise, ARX models with quantized measurements or errors-in-variables identification. In this paper, an algorithm is proposed for bounding nonconvex feasible sets, by exploiting the specific structure of the considered parametric models.