A Projected Stochastic Approximation Method for Adaptive Filters and Identifiers

摘要

This report deals with a great variety of stochastic approximation procedures, for constrained and unconstrained systems and for convergence w.p.1. and weak convergence, all for systems with correlated inputs. The techniques are readily usable for many problems that are not explicitly treated there. This will be illustrated here for one particular class of constrained problems which is of great current interest and which arises in identification and in adaptive control theory. In fact, it is just such constrained problems to which more attention should be given, owing to their prevalence. The proofs are contained in various parts and, after the problem is defined, it is shown how to put the bits and pieces together. The problem and method are typical of a large class of adaptive systems which can be treated by similar methods, and is worth singling out.