Adaptive control: Towards a complexity-based general theory

Two recent developments are pointing the way towards an input-output theory of H-infinity-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-infinity); and (2) optimally fast identification in H-infinity on the other. Taken together, these are yielding adaptive algorithms for slowly varying data in H-infinity-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.