Strong consistency of parameter estimates in direct self-tuning control algorithms based on stochastic approximation

Abstract

In this paper convergence of the regulator parameter estimates generated by direct self-tuning control algorithms of stochastic approximation type is considered. The process is supposed to be represented by an ARMAX model with an arbitrary delay, while a dither signal converging to zero in the mean-square sense is superimposed on a deterministic reference. The strong consistency of the regulator parameter estimates is proved under assumptions concerning the estimator complexity and the properties of the optimal regulator transfer function for a broad class of dither signals. The impact of a priori information on the dimension of the estimator and the consistency of the parameter estimates is indicated. It is demonstrated that the classical persistence of excitation condition is not satisfied for the analyzed algorithms.