Adaptive feedback, identification and complexity: an overview

Two recent developments are surveyed, which are pointing the way towards an input-output theory of H^∞-l¹ adaptive feedback. The problems involve: (1) feedback performance (exact) optimization under large plant uncertainty (the two-disc problem of H^∞); and (2) optimally fast identification in H^∞. The two problems result in adaptive algorithms for slowly varying data in H^∞-l¹. 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