Learning models from data: the set membership approach

The problem of identifying complex linear systems from noise corrupted data is investigated, considering that only approximate models can be estimated and the effects of unmodeled dynamics have to be accounted for. The paper presents a unified view of the set membership identification theory, as recently evolved by the author et al. (1997), aiming to deliver not only a model of the system to be identified, but also a measure of its approximation. Optimality and convergence results are reported, related to identification problems for different settings of experimental conditions and noise assumptions.