Temporal Logic Resilience for Continuous-time Systems

TL;DR

This paper introduces a new framework for quantifying the resilience of continuous-time nonlinear systems to external disturbances while satisfying temporal logic specifications, using scenario optimization for computation.

Contribution

It presents a novel approach to measure and compute the maximum disturbance a system can tolerate, extending robustness concepts with a resilience metric.

Findings

Derived bounds on perturbed trajectories for nonlinear systems.

Developed a scenario optimization-based computational method.

Validated approach through diverse case studies.

Abstract

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.