On robustness to noise of least squares based adaptive control

Abstract

Current engineering practice for adaptive control schemes is to base the design on globally convergent schemes for simple plant models. An important class of such schemes uses least squares estimation of assumed simple input-output models and constructs the controller using the parameter estimates. This paper studies the robustness of such schemes to the presence of unmodelled plant coloured noise. Such noise is sometimes an adequate model for unmodelled plant dynamics. The theory of the paper makes a connection between the least squares parameter error equations and those associated with extended least squares using a posteriori noise estimates for which there are known global convergence results. For the case of adaptive minimum variance control of minimum phase plants, this connection permits stronger convergence results than those hitherto derived from the theory of extended least squares based on a priori noise estimates.