Runtime Monitoring of Distributed Cyber-Physical Systems Without a Global Clock

2026-08-13

AI Summary

This work addresses the challenge of runtime monitoring in distributed cyber-physical systems, which lack a global clock and thus cannot readily employ dense-time temporal logics. The paper presents the first continuous monitoring algorithm tailored for environments without global time synchronization, enabling behavior verification with global temporal semantics by mapping Signal Temporal Logic (STL) specifications onto local drifting clocks. The key innovation lies in extending the notion of satisfaction signals under a partially synchronous clock model and integrating multidimensional temporal geometric analysis to support an expressive STL fragment containing full timed temporal operators. Theoretical analysis provides worst-case complexity bounds, and empirical evaluation demonstrates that the approach scales efficiently to 50 agents, with validation in both drone formation and smart grid scenarios.

Abstract

We give the first theoretical characterization, and the first algorithm, for continuous monitoring of a distributed Cyber-Physical System (CPS) against a dense-time temporal logic specification. A distributed CPS is composed of multiple agents, each with a local clock; these clocks drift from each other, so there is no well-defined global time. When monitoring such a system's output signal against a temporal logic specification, it is not evident how to interpret the temporal constraints of the formula, and what satisfaction means. Yet CPS designers, like control engineers, typically think of their system's operation in terms of global time. Most existing techniques for monitoring distributed systems work with discrete-time specifications not suitable for CPS, and/or require an explicit mapping of temporal constraints to local clocks. We introduce an algorithm that addresses the above challenges for a fragment of Signal Temporal Logic (STL) that still includes all temporal operators. It relies on a novel extension of satisfaction signals to this partially synchronous setting (where clocks drift), and an analysis of the geometry of multi-dimensional partially synchronous time. The algorithm returns the set of all possible global moments that can satisfy the specification. Knowledge of these possible global moments is important for debugging distributed hybrid control systems such as fleets of drones and electrical grids. We derive the worst-case complexity of the algorithm, and implement a sound approximation of it that experimentally illustrates effective monitoring, even in scenarios of up to 50 agents.

Problem

• distributed Cyber-Physical Systems
• runtime monitoring
• global clock
• temporal logic
• clock drift

Innovation

• distributed cyber-physical systems
• runtime monitoring
• Signal Temporal Logic
• clock drift
• partial synchrony