Robustness of a Derivative-Free Adaptive Control Law in the Presence of Unmodeled Dynamics

Although adaptive control theory offers mathematical tools to achieve required system performance without excessive dependence on modeling, its application to safety-critical systems can be limited by the presence of unmodeled dynamics. This paper examines the robustness to unmodeled dynamics of a recently developed derivative-free adaptive control law. In contrast to derivative-based adaptive laws it is shown, using a LyapunovKrasovskii functional, that robustness to unmodeled dynamics is improved by increasing the adaptation gain. This is accomplished by including a bias term in the set of basis functions employed by the adaptive control law. It is shown that derivative-based adaptive laws do not offer the same advantage. Examples are presented that compare the these two forms of adaptation in the context of sensitivity to unmodeled dynamics.