Introduction

An overview of stochastic adaptive control from its birth to date is provided. In particular, the concept of Certainty Equivalence (CE) adaptive control is highlighted together with the fact that in some of its principal forms it requires consistent parameter estimation. Since sample-path Persistent Excitation (PE) of the associated regression vector process ensures consistency, various attempts to secure that property are discussed. The PE requirement may be abandoned when certain control-biased estimation methods are utilized. One such methodology is realized in this work which is built upon a geometric study of limit sets of parameter estimates which give rise to closed-loop indistinguishable dynamics.