Robust Data-Driven Control Barrier Functions for Unknown Continuous Control Affine Systems

In this letter, we introduce robust data-driven control barrier functions (CBF-DDs) to guarantee robust safety of unknown continuous control affine systems despite worst-case realizations of generalization errors from prior data under various continuity assumptions. To achieve this, we leverage non-parametric data-driven approaches for learning guaranteed upper and lower bounds of an unknown function from the data set to formulate/obtain a safe input set for a given state. By incorporating the safe input set into an optimization-based controller, the safety of the system can be ensured. Moreover, we present several complexity reduction approaches including providing subproblems that can be solved in parallel and downsampling strategies to improve computational performance.