Adaptive control: Towards a complexity-based general theory (Q1298278)

In this tutorial overview, the author demonstrates that his recent work (some of it jointly with Lin, Owen and Wang) in the \(H^\infty\)-framework provides means of computing adaptive controllers for systems in the \(H^\infty/l^1\) ``slowly time-varying'' class. More generally, it is outlined how, at a conceptual level, these results motivate a general input-output theory linking identification, adaptation and control learning. The author gives a definition of adaptation which is based on system performance under uncertainty, and is independent of internal structure, presence or absence of variable parameters, or even feedback. In this context, the concepts of metric complexity (such as metric dimension and metric entropy) play an imporatant rôle as indicators of the size of the plant's set of uncertainty.