UNMODELED DYNAMICS IN ADAPTIVE-CONTROL SYSTEMS REVISITED

An alternative approach to analyze the robustness of adaptive systems with respect to unmodeled dynamics and external disturbances is presented. It is shown that an adaptation algorithm using a variable sigma-factor, equivalent to a constant sigma-factor together with projection, can provide a globally asymptotically stable system with respect to a compact residual set, under mild requirements. Conditions are given to ensure small tracking error, particularly in the case of fast adaptation. The approach also allows to show that certain restrictive assumptions needed earlier can in fact be discarded.