  Motivated by the lack of systematic tools to obtain safe control laws for
hybrid systems, we propose an optimization-based framework for learning
certifiably safe control laws from data. In particular, we assume a setting in
which the system dynamics are known and in which data exhibiting safe system
behavior is available. We propose hybrid control barrier functions for hybrid
systems as a means to synthesize safe control inputs. Based on this notion, we
present an optimization-based framework to learn such hybrid control barrier
functions from data. Importantly, we identify sufficient conditions on the data
such that feasibility of the optimization problem ensures correctness of the
learned hybrid control barrier functions, and hence the safety of the system.
We illustrate our findings in two simulations studies, including a compass gait
walker.

Systems and Control;Machine Learning;Systems and Control;Optimization and Control