Robustness and perfect tracking in simple adaptive control

Abstract

SummaryAdaptive 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.