Robustness of adaptive control without deadzones, data normalization or persistence of excitation

Abstract

Robustness properties have been established for modified adaptive control algorithms. The major modifications involve various combinations of normalization, (relative) deadzones, persistence of excitation, parameter projection and/or so-called σ-modification. Results showing global boundedness have used some form of data normalization. Many results on local properties have depended on persistence of excitation. However, use of these modifications involve some a priori knowledge of the plant for good performance. This may lead to complications in practice. Here it is shown that some useful local robustness properties hold if only parameter projection is used as a modification of the basic gradient estimator.