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Adaptive regulation of MIMO linear systems against unknown sinusoidal exogenous inputs
Author(s) -
Ficocelli Maurizio,
Ben Amara Foued
Publication year - 2009
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.1072
Subject(s) - control theory (sociology) , parameterized complexity , regulator , decoupling (probability) , mimo , adaptive control , controller (irrigation) , linear system , computer science , mathematics , control engineering , engineering , algorithm , control (management) , artificial intelligence , computer network , agronomy , biochemistry , chemistry , channel (broadcasting) , mathematical analysis , biology , gene
This paper deals with the adaptive regulation problem in linear multi‐input multi‐output systems subject to unknown sinusoidal exogenous inputs, where the frequencies, amplitudes, and phases of the sinusoids are unknown and where the number of sinusoids is assumed to be known. The design of an adaptive regulator for the system under consideration is performed within a set of Q ‐parameterized stabilizing controllers. To facilitate the design of the adaptive regulator, triangular decoupling is introduced in part of the closed‐loop system dynamics. This is achieved through the proper selection of the controller state feedback gain and the structure of the Q parameter. Regulation conditions are then presented for the case where the sinusoidal exogenous input properties are known. For the case where the sinusoidal exogenous input properties are unknown, an adaptation algorithm is proposed to tune the Q parameter in the expression of the parameterized controller. The online tuning of the Q parameter allows the controller to converge to the desired regulator. Convergence results of the adaptation algorithm are presented. A simulation example involving a retinal imaging adaptive optics system is used to illustrate the performance of the proposed adaptive system. Copyright © 2008 John Wiley & Sons, Ltd.