Quantifying the Safety of Trajectories by the Data Corruption Needed to Crash

Abstract.

This work quantifies the safety of trajectories of a dynamical system by the perturbation intensity required to render a system unsafe (crash into the unsafe set). In the data-driven setting, this perturbation intensity can be interpreted as the minimal data corruption required for a data-consistent model to crash. Computation of this measure of safety is posed as a peak-minimizing optimal control problem. Convergent lower bounds on the minimal peak value of controller effort are computed using polynomial optimization and the moment-Sum-of-Squares hierarchy.