Convergence and rate of convergence of a recursive identification and adaptive control method which uses truncated estimators

A stochastic approximation-like method is used for the recursive identification of the coefficients in , where is a sequence of mutually independent and bounded random variables, and is independent of the bounded . Such methods normally require the recursive estimation of the "residuals" or the , and the algorithms for doing this can be unstable if the parameter estimates are not close enough to their true values. The problem is solved here by use of a simple truncated estimator, which is probably what would be used in implementation in any, case. Then, under a stability, and strict positive real type condition, with probability 1 (w.p.1) convergence is proved and the rate of convergence is obtained. An associated adaptive control problem is also treated.