A Barrier-Based Scenario Approach to Verifying Safety-Critical Systems

We detail an approach to safety-critical verification using barrier functions. Our method requires limited system data verify a system's ability keep positive candidate function $h$ at discrete-time intervals over its trajectories. Specifically, our first randomly samples initial conditions and parameters for controlled, continuous-time records the state trajectory discrete intervals. Then, we evaluate these states under determine constraints randomized linear program. The solution this program provides either probabilistic statement in aforementioned vein or counterexample - instance where went unsafe. To showcase results, robotarium simulator, identify counterexamples hardware counterpart, experimentally safety of multi-agent quadrupedal system.