Robust Approximate Modeling from Noisy Point Evaluations

We consider approximate modeling of stable linear shift-invariant systems in the H
^∞
sense from approximate point evaluations at approximately known frequencies. Two error structures for the point evaluations are studied: pointwise bounded error and a certain error averaging structure. A main motivation for the present work comes from currently active research problems concerning modeling for robust control design from experimental data. Several results are given on various aspects of approximation algorithm performance, and on robust convergence. A constrained least absolute deviations method based on minimizing the value of the error averaging prior subject to a model prior restricting the complexity of the behaviour of the model is proposed. This linear programming method is a strongly optimal algorithm within factor two with respect to the model and error priors used in its construction. Relationships between problems of identification of nominal models and uncertainty modeling are studied.