Temporal Logic Resilience for Continuous-time Systems
For control systems engineers, it provides a method to quantify resilience, a safety-critical metric, but the approach is incremental as it builds on existing robustness concepts.
This paper introduces a framework to compute a lower bound on the maximum disturbance a continuous-time system can tolerate while satisfying signal temporal logic specifications, validated on several case studies.
In this paper, we present a novel framework for quantifying a lower bound on resilience in continuous-time (non)linear systems subject to external disturbances while ensuring satisfaction of signal temporal logic specifications. Unlike robustness, which evaluates how well a system satisfies a specification under a given disturbance, resilience measures the maximum disturbance a system can tolerate from a given initial state while maintaining specification satisfaction. We first derive bounds on the perturbed trajectories and then use them to formulate a computational method based on scenario optimization to efficiently compute the maximum admissible disturbance. We validate our approach through case studies, including dc motor, temperature regulation, a nonlinear numerical example, and a vehicle collision avoidance case.