Extended least squares and their applications to adaptive control and prediction in linear systems

Herein strong consistency of recursive extended least squares is established under considerably weaker assumptions than previously assumed in the literature. The argument used to establish consistency also leads to certain basic properties of adaptive predictors based on these recursive estimators. Making use of these properties of the adaptive predictors, simple modifications of the Åström-Wittenmark self-tuning regulator are proposed and shown to be asymptotically optimal.