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

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.