Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 299-329
doi:10.1155/DDNS.2005.299
Adaptive control of single-input single-output hybrid
systems possessing interacting discrete- and
continuous-time dynamics
Department of Electricity and Electronics, Faculty of Science and Technology, University of Basque Country, Leioa (Bizkaia), Aptdo, 644 de Bilbao, Spain
Received 26 January 2005
Copyright © 2005 M. de la Sen. 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 the problem of synthesizing a
robust adaptive controller for a specific class of single-input
single-output (SISO) time-invariant hybrid controlled object
(plant) which can operate under bounded disturbances and/or
unmodeled dynamics. The hybrid plant dealt with is composed of two
coupled subsystems, one of them being of continuous-time type
while the other is digital. As a result there are also mixed
continuous-time and discrete signals present in the system
associated either with the solutions of differential equations
which depend at the same time on both discrete-time and
continuous-time forcing terms and on generalized
difference equations associated with discretized and digital
signals. The estimation algorithm is of a continuous-time nature
since the plant parameter estimates are updated for all time. It
also incorporates a relative adaptation dead-zone as a robust
stabilization mechanism which prevents against instability in the
presence of a common class of unmodeled dynamics and bounded
noise.