Abstract
While the original classical parameter adaptive controllers do not handle noise or unmodelled dynamics well, redesigned versions have been proven to have some tolerance; however, exponential stabilization and a bounded gain on the noise are rarely proven. Here we consider a classical pole placement adaptive controller using the original projection algorithm rather than the commonly modified version; we impose the assumption that the plant parameters lie in a convex, compact set, although some progress has been made at weakening the convexity requirement. We demonstrate that the closed-loop system exhibits a very desirable property: there are linear-like convolution bounds on the closed-loop behaviour, which confers exponential stability and a bounded noise gain, and which can be leveraged to prove tolerance to unmodelled dynamics and plant parameter variation. We emphasize that there is no persistent excitation requirement of any sort; the improved performance arises from the vigilant nature of the parameter estimator.