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Mathematical Theory of Feedback Organizations

This project is inspired by developments in feedback theory which have taken place over the last decade. Based on the mathematical concepts of Hardy Spaces ([{_inline}$H^infty${_inline}]) which, for the first time, have made the action of feedback on unstructured plant uncertainty explicitly accessible. They have provided new tools for the control of systems for which the only available models are approximate or crude. The objectives of this project are, first of all, to consolidate the new developments and, in the longer term, to exploit them in order to prepare the basis for a theory of hierarchical feedback organizations. Such a theory would have a potential for impact on the areas of artificial intelligence, information processing, and large-scale systems. Recently, the emphasis has been on two problem areas which are affected by the developments in feedback theory. The first involves a re-examination of adaptive control and identification. This is an elusive subject which has defied systematic formulation in the past. The recent work has led to what is believed to be the first general definition of control adaptation, based on notions of metric complexity. Key components of a general theory of optimal adaption have been achieved for slowly time-varying systems. The current focus is on a new look at identification in the [{_inline}$H^infty${_inline}] setting. The second problem is concerned with nonparametric model uncertainty. Fresh approaches to design in the face of such uncertainty are being developed.

G. Zames

Thierry Baron
Mon Nov 13 10:43:02 EST 1995