Quantifying the Safety of Trajectories using Peak-Minimizing Control

TL;DR

This paper introduces a method to quantify trajectory safety by calculating the minimal control effort needed to cause a system to crash, using peak-minimizing optimal control and polynomial optimization, with extensions to data-driven safety analysis.

Contribution

It presents a novel peak-minimizing optimal control framework for safety quantification and extends it to data-driven scenarios using moment-Sum-of-Squares hierarchy.

Findings

Computed convergent lower bounds on control effort for safety.

Extended safety analysis to data corruption scenarios.

Demonstrated effectiveness through theoretical and computational results.

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). 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. The crash-safety framework is extended towards data-driven safety analysis by measuring safety as the maximum amount of data corruption required to crash into the unsafe set.