On the effect of input filtering and fast adaptation in model reference adaptive control

In recent years we have witnessed the publication in various control and applications journals of some papers where it is suggested to add to the standard model reference adaptive controller an input filter and to use high adaptation gains. It has been claimed that these modifications improve the performance of the system. The purpose of this brief note is to discuss these claims. A key contribution of the paper is the proof that parameter adaptation “freezes” as the adaptation gain goes to infinity-effectively stopping the stabilization (or performance improvement) mechanism due to adaptation.