Robustness of adaptive control systems to unmodeled dynamics : a describing function viewpoint

Abstract

Recently, it was shown that a standard model reference adaptive controller modified with a suitably tuned projection algorithm ensures robustness (global boundedness) of the overall adaptive system to a class of unmodeled dynamics with minimal restrictions. However, extensive first-principle based arguments and/or analysis of the parameter trajectory is employed. An alternative to such analysis, albeit approximate, is to use the well-known Describing Function (DF) method. In doing so, the analysis of the robust adaptive control problem becomes tractable and resembles that of familiar and classical linear stability analysis.