Robustness of a Derivative-Free Adaptive Control Law

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 Lyapunov-Krasovskii 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 these two forms of adaptation in the context of sensitivity to unmodeled dynamics.