Learning Safe Data-Driven Control Barrier Functions for Unknown Continuous Systems

This letter presents a semi-parametric approach for learning safe data-driven control barrier functions (SDD-CBFs) for unknown continuous systems from noisy data. By leveraging optimization theory, interval and mixed-monotone bounding, and probably approximately correct (PAC) learning, we learn at design time both parametric control barrier functions (CBFs) and their non-parametric CBF conditions from noisy data with a mixed-integer linear program (MILP) to ensure robust safety despite generalization errors with a high probability. Moreover, we propose an online safety filter for minimally modifying any nominal controller for safety that reduces to computationally efficient quadratic programming.