Global stability of adaptive pole placement algorithms

Abstract

This paper presents direct and indirect adaptive control schemes for assigning the closed-loop poles of a single-input, single-output system in both the continuous- and discrete-time cases. The resulting closed-loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids. In particular, persistent excitation of the potentially unbounded closed-loop input-output data, and hence convergence of a sequential least-squares identification algorithm is proved. The results are applicable to standard sequential least squares, and least squares with covariance reset.