Optimal and suboptimal H2 and H∞ estimators for set membership identification

Identification of mixed parametric/nonparametric models is addressed, in the framework of set membership identification and information-based complexity. It is assumed that errors are partly due to disturbances affecting the system, and partly to discrepancies between the parametric model and the actual system. This argument leads to enlarging the model class by adding a nonparametric part, usually consisting of a linear operator bounded in an appropriate norm. In this paper, we assume that measurements provide information only on the first samples of the system impulse response. In particular, in our set-theoretic context, the optimal approximation amounts to computing the centers of sets, constrained to belong to a lower dimensional subspace. H₂ and H_∞ worst-case identification errors are considered and the corresponding conditional center problems addressed. Comparisons with suboptimal estimators are also reported.