Maintaining safety under adaptation has long been considered to be an important capability for autonomous systems. As these systems estimate and change the ego-model of the system dynamics, questions regarding how to develop safety guarantees for such systems continue to be of interest. We propose a novel robust safe control methodology that uses set-based safety constraints to make a robotic system with dynamical uncertainties safely adapt and operate in its environment. The method consists of designing a scalar energy function (safety index) for an adaptive system with parametric uncertainty and an optimization-based approach for control synthesis. Simulation studies on a two-link manipulator are conducted and the results demonstrate the effectiveness of our proposed method in terms of generating provably safe control for adaptive systems with parametric uncertainty.
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