Temporal Robustness of Stochastic Signals

TL;DR

This paper introduces the concepts of synchronous and asynchronous temporal robustness for stochastic signals, assesses their risks, and demonstrates their application in autonomous driving scenarios, enhancing understanding of timing uncertainties.

Contribution

It defines temporal robustness for stochastic signals, introduces risk assessment methods, and applies these concepts to real-world autonomous driving case studies.

Findings

Temporal robustness metrics effectively quantify timing uncertainties.

Temporal robustness risk can be estimated from data using value-at-risk.

Case studies demonstrate practical applicability in autonomous driving scenarios.

Abstract

We study the temporal robustness of stochastic signals. This topic is of particular interest in interleaving processes such as multi-agent systems where communication and individual agents induce timing uncertainty. For a deterministic signal and a given specification, we first introduce the synchronous and the asynchronous temporal robustness to quantify the signal's robustness with respect to synchronous and asynchronous time shifts in its sub-signals. We then define the temporal robustness risk by investigating the temporal robustness of the realizations of a stochastic signal. This definition can be interpreted as the risk associated with a stochastic signal to not satisfy a specification robustly in time. In this definition, general forms of specifications such as signal temporal logic specifications are permitted. We show how the temporal robustness risk is estimated from data for the value-at-risk. The usefulness of the temporal robustness risk is underlined by both theoretical and empirical evidence. In particular, we provide various numerical case studies including a T-intersection scenario in autonomous driving.