Adaptive control with discontinuous σ-factor and saturation for improved robustness

An adaptive control law is proposed to improve the robustness of the adaptive system with respect to fast unmodelled dynamics represented by a singular perturbation. The new law is based on saturation of the regressor and control parameter vector with inclusion of a discontinuous σ-factor. The analysis of the resulting system is presented and the conclusions are illustrated by simulations. The introduction of a discontinuous σ-factor represents an extension of an earlier work. The advantages of this extension include global stability, with less restrictive assumptions, and better transient behaviour.