  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.
