  This paper introduces the Generalized Action Governor, which is a supervisory
scheme for augmenting a nominal closed-loop system with the capability of
strictly handling constraints. After presenting its theory for general systems
and introducing tailored design approaches for linear and discrete systems, we
discuss its application to safe online learning, which aims to safely evolve
control parameters using real-time data to improve performance for uncertain
systems. In particular, we propose two safe learning algorithms based on
integration of reinforcement learning/data-driven Koopman operator-based
control with the generalized action governor. The developments are illustrated
with a numerical example.
