Optimal Hankel-norm identification of dynamical systems

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 allows for a notion of misfit of dynamical systems that 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. Sets of Pareto-optimal models are defined as feasible trade-offs between complexity and misfit of models, and it is shown how all Pareto-optimal models are characterized as exact models of compressed data sets obtained from Hankel-norm approximations of data matrices. This leads to new conceptual algorithms for optimal approximate identification of time series