The Caratheodory-Fejer problem and H∞ identification: a time domain approach

Addresses a worst-case, robust control oriented identification problem. This problem is a variant in the general framework of H_∞ identification problems which have been studied by several authors. In this problem the available a priori information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The plant to be identified is assumed to lie in a certain subset in the space of H_∞. The available experimental information consists of a corrupt finite output time series obtained in response to a known nonzero but otherwise arbitrary input. The objective is to identify from the given a priori and experimental information an uncertain model which includes a nominal plant model in H _∞ and a bound on the modeling error measured in H_∞ norm. The authors present both an identification error and several explicit lower and upper bounds on the identification error. The proposed algorithm is in the class of interpolatory algorithms which are known to posses desirable optimality properties in reducing the identification error. This algorithm may be obtained by solving an extended Caratheodory-Fejer problem via standard convex programming methods. The error bounds not only provide explicit estimates on the modeling error, but also are used to establish the convergence properties of the proposed identification algorithm