Robustness and perfect tracking in simple adaptive control. (19th May 2015)

• Record Type: Journal Article
• Authors: Barkana, Itzhak
• Other Names: Oliveira Tiago Roux guestEditor.; Fridman Leonid guestEditor.; Ortega Romeo guestEditor.
• Is Part Of: International journal of adaptive control and signal processing. Volume 30:Number 8/10(2016:Aug/Oct.)
• Page Start: 1118
• Page End: 1151
• Publication Date: 2015-05-19
• Subjects: simple adaptive control -- stability -- nonlinear systems -- robustness -- autonomous and nonautonomous systems; Adaptive control systems -- Periodicals; Adaptive signal processing -- Periodicals; 629.836
• DOI: 10.1002/acs.2573
• Languages: English
• ISSNs: 0890-6327

Abstract

Summary: Adaptive controllers have been developed to guarantee stability and asymptotically perfect tracking under ideal conditions. In particular, the simple adaptive control methodology has been developed to avoid the use of identifiers, observer‐based controllers and, in general, to avoid using large order adaptive controllers in the control loop. In spite of initially successful applications, it is known that the basic adaptive algorithm may lead to divergence of the adaptive gains in such non‐ideal conditions as the presence of disturbances. A sigma‐term adjustment has been used to maintain boundedness with disturbance, yet is known that it seems to also eliminate perfect following even in ideal situations. Furthermore, bursting and other chaotic‐like phenomena observed in connection with the sigma‐term may also give pause to potential users of adaptive control. This paper revisits and modifies the use of various components of the simple adaptive control approach and shows how one can use passivity concepts such that, while it maintains robustness with disturbances, it also allows asymptotically perfect tracking in ideal conditions. Copyright © 2015 John Wiley & Sons, Ltd.