A New Adaptive Law for Robust Adaptation without Persistent Excitation

A new adaptive law motivated by that given in [1] is proposed for the robust adaptive control of plants with unknown parameters. In this adaptive law the output error el plays a dual role in the adjustment of the control parameter vector. In the ideal case the adaptive system has bounded solutions; in addition the error equations are uniformly asymptotically stable in the large when the reference input is sufficiently persistently exciting. The adaptive system is also shown to be robust under bounded external disturbances. Finally it is shown that, by suitably modifying the adaptive law, the overall system can be made robust in the presence of unmodeled dynamics of the plant.