Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 1, Pages 31-67

Robustly stable multiestimation scheme for adaptive control and identification with model reduction issues

A. Bilbao-Guillerna, M. De La Sen, A. Ibeas, and S. Alonso-Quesada

Instituto de Investigación y Desarrollo de Procesos, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Campus de Leioa (Bizkaia), Apartado 644, Bilbao 48080, Spain

Received 17 May 2004

Copyright © 2005 A. Bilbao-Guillerna et al. 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.


A discrete pole-placement-based and multiestimation-based adaptive control scheme involving a relative adaptation dead zone is presented for a plant with known poles and unknown zeros. The basic usefulness of the proposed multiestimation scheme is related to the use of a set of models of reduced order associated with the multiestimation scheme instead of a high-order one. Depending on the frequency spectrum characteristics of the input and on the estimates evolution, the multiestimation scheme selects on-line the most appropriate model and its related estimation scheme in order to improve the identification and control performances. Robust closed-loop stability is proved even in the presence of unmodeled dynamics of sufficiently small sizes as it has been confirmed by simulation results. The scheme chooses in real time the estimator/controller associated with a particular reduced model possessing the best performance according to an identification performance index by implementing a switching rule between estimators. The switching rule is subject to a minimum residence time at each identifier/adaptive controller parameterization for closed-loop stabilization purposes. A conceptually simple higher-level supervisor, based on heuristic updating rules which estimate on-line the weights of the switching rule between estimation schemes, is discussed.