Self-tuning control based on generalized minimum variance criterion for auto-regressive models

Theoretical problems on self-tuning control include stability, performance and convergence of the recursive algorithm involved. In this paper, the problem of controlling minimum or non-minimum phase auto-regressive models with constant but unknown parameters is considered. The stability of an algorithm obtained by combining a recursive estimator for the controller parameters and a generalized minimum variance criterion is proved. The main result is the theorem which assures the overall stability for the closed-loop system in presence of white noise in the input–output relation, where the estimated parameters do not necessarily converge to the true values. The algorithm is proved by the Lyapunov theory.