Optimal approximate model identification in the Hankel norm

A method of optimal approximate system identification is proposed using a distance measure between an exact model for the observed data sequences and a reduced order (approximate) model for the same data but of lower complexity. A key property of this measure is that the distance is independent of specific parameterizations of the model. This distance measure can be computed in terms of induced norms of Hankel operators which are associated with the data. Using these ideas and a behavioral framework of describing dynamical systems, we put forward a new algorithm for optimal approximate identification of time series. Keywords: System identification, approximate modeling, Hankel operators, behavioral theory.