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Discrete Dynamics in Nature and Society
Volume 2006, Article ID 41973, 27 pages
http://dx.doi.org/10.1155/DDNS/2006/41973

Adaptive control of time-invariant systems with discrete delays subject to multiestimation

Instituto de Investigación y Desarrollo de Procesos, Facultad de Ciencias, Universidad del País Vasco, Aparatado 644 de Bilbao, Leioa(Bizkaia) 48080, Spain

Received 14 November 2005; Accepted 27 February 2006

Copyright © 2006 M. De la Sen and S. Alonso. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with a robustly stable adaptive pole-placement-based controller for time-delay linear systems with unknown point delays within known intervals of sufficiently small lengths under unmodeled dynamics and bounded disturbances. A multiestimation scheme is used to improve the identification error and then to deal with possible errors between the true basic delays compared to that used in the regressor of the adaptive scheme. Each estimation scheme possess a relative dead zone for each estimation scheme which freezes the adaptation for small sizes of the adaptation error compared with the estimated size of the contribution of the uncertainties to the filtered output. All the estimation schemes run in parallel but only that, which is currently in operation, parameterizes the adaptive controller to generate the plant input at each time. A supervisory scheme chooses in real time the appropriate estimator subject to a minimum residence time which is the tool to ensure closed-loop stability under switching between the estimators in the estimation scheme. The dead zone adaptation mechanism prevents the closed-loop system against potential instability caused by uncertainties.