Abstract
Classical discrete-time adaptive controllers typically provide asymptotic stabilization and tracking; usually the affect of the noise is at best bounded-input bounded-output. Recently we have shown that if you design a discrete-time adaptive controller in just the right way, then in a variety of situations you not only obtain exponential stability, but also a bounded gain on the noise in every p-norm, as well as a never-before-seen linear-like convolution bound on the input-output behavior. Quite surprisingly, the approach is very natural, and relies on the use of the unmodified, original projection algorithm to carry out parameter estimation; if the set of plant uncertainty is not convex, then a multi-estimator and switching are used. The goal of this paper is to provide an overview of the approach, discuss the results-to-date, and list some of the open problems.