The problem of optimal approximate system identification is addressed with a newly defined measure of misfit between observed time series and linear time-invariant models. The behavioral framework is used as a suitable axiomatic setting for a non-parametric introduction of system complexity and a notion of misfit of dynamical systems which is independent of system representations. The misfit function introduced here is characterized in terms of the induced norm of a Hankel operator associated with the data and a co-inner kernel representation of a model. Two optimal approximate identification problems are considered in this framework. New conceptual algorithms are proposed for optimal approximate identification of time series.
Key Words: System identification, approximate modeling, Hankel operators, behavioral theory, linear systems.