A robust stochastic adaptive controller

Abstract

The adaptive tracking problem is considered for discrete-time stochastic systems consisting of a modeled part being a stable ARMAX process and unmodeled dynamics dominated by a small constant epsilon multiplied by a quantity independent of epsilon but tending to infinity as the past input, output, and noise grow. The adaptive control law proposed is switched at stopping times and is disturbed by a sequence of random vectors bounded by an arbitrary small but fixed constant sigma . It is shown that the closed-loop system is globally stable, the estimation errors for parameters contained in the modeled part of the order epsilon , and the tracking error differs from the minimum tracking error for systems without unmodeled dynamics by value of O( epsilon /sup 2/)+O( sigma /sup 2/).