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

Authors:
Anna Patete;Katsuhisa Furuta;Masayoshi Tomizuka
Affiliations:
Tokyo Denki University, Department of Advanced Multidisciplinary Engineering, Hatoyama Hikigun, Saitama, 350-0394, Japan;Tokyo Denki University, Department of Computer and Systems Engineering, Hatoyama Hikigun, Saitama, 350-0394, Japan;University of California, Berkeley, Department of Mechanical Engineering, CA, 94720, USA
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

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.