Near supermartingales for convergence analysis of recursive identification and adaptive control schemes

An equivalent stochastic feedback system can be associated to many recursive identification and adaptive control schemes. This equivalent feedback system has a certain structure which is used for constructing near supermartingales allowing to establish a.s. convergence. Explicit convergence conditions are then obtained for recursive identification and adaptive control schemes which admit an equivalent stochastic feedback representation of the form considered. The usefulness of the results is llustrated by their application to the straightforward convergence analysis of Several schemes.