Abstract
Two recent developments will be surveyed here which are pointing the way towards an input–output theory of H ∞- l 1 adaptive feedback: The solution of problems involving; (1) feedback performance (exact) optimization under large plant uncertainty on the one hand (the two-disc problem of H ∞); and (2) optimally fast identification in H ∞ on the other. Taken together, these are yielding adaptive algorithms for slowly varying data in H ∞- l 1. At a conceptual level, these results motivate a general input-output theory linking identification, adaptation, and control learning. In such a theory, the definition of adaptation is based on system performance under uncertainty, and is independent of internal structure, presence or absence of variable parameters, or even feedback.
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