Title :
A Representation Theorem for the Error of Recursive Estimators
Author :
Gerencsér, László
Author_Institution :
Comput. & Autom. Res. Inst., Hungarian Acad. of Sci., Budapest
Abstract :
The objective of this paper is to present advanced and less known techniques for the analysis of performance degradation due to statistical uncertainty for a wide class of linear stochastic systems in a rigorous and concise manner. The main technical advance of the present paper is a strong approximation theorem for the Djereveckii-Fradkov-Ljung (DFL) scheme with enforced boundedness, in which, for any q ges 1, the Lq-norms of the so-called residual terms are shown to tend to zero with rate N-frac12-epsiv with some epsiv > 0. This is a significant extension of previous results for the recursive prediction error or RPE estimator of ARMA processes given in [L. Gerencser, Systems Control Lett., 21 (1993), pp. 347-351. Two useful corollaries will be presented. In the first a standard transform of the estimation-error process will be shown to be L-mixing. In the second the asymptotic covariance matrix of the estimator will be given. An application to the minimum-variance self-tuning regulator for ARMAX systems will be described
Keywords :
autoregressive moving average processes; covariance matrices; linear systems; poles and zeros; recursive estimation; self-adjusting systems; stochastic systems; ARMA processes; Djereveckii-Fradkov-Ljung scheme; asymptotic covariance matrix; linear stochastic systems; minimum-variance self-tuning regulator; performance degradation; recursive estimators; recursive prediction error; representation theorem; statistical uncertainty; Adaptive control; Approximation algorithms; Chromium; Control systems; Degradation; Performance analysis; Recursive estimation; Stochastic processes; Stochastic systems; Uncertainty;
Conference_Titel :
Decision and Control, 2006 45th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
1-4244-0171-2
DOI :
10.1109/CDC.2006.377578
