Distributionally Robust Cascading Risk in Multi-Agent Rendezvous: Extended Analysis of Parameter-Induced Ambiguity

TL;DR

This paper presents a theoretical framework for analyzing the distributionally robust risk of cascading failures in multi-agent rendezvous systems, accounting for parameter uncertainties, delays, and noise, with validated simulations.

Contribution

It introduces a novel conditional distributionally robust functional and closed-form risk expression for multi-agent safety under uncertainty, delays, and noise.

Findings

Closed-form risk expression derived for multi-agent systems

Risk sensitivity patterns identified for system design

Simulations validate theoretical risk bounds

Abstract

Ensuring safety in autonomous multi-agent systems during time-critical tasks such as rendezvous is a fundamental challenge, particularly under communication delays and uncertainty in system parameters. In this paper, we develop a theoretical framework to analyze the \emph{distributionally robust risk of cascading failures} in multi-agent rendezvous, where system parameters lie within bounded uncertainty sets around nominal values. Using a time-delayed dynamical network as a benchmark model, we quantify how small deviations in these parameters impact collective safety. We introduce a \emph{conditional distributionally robust functional}, grounded in a bivariate Gaussian model, to characterize risk propagation between agents. This yields a \emph{closed-form risk expression} that captures the complex interaction between time delays, network structure, noise statistics, and failure modes. These expressions expose key sensitivity patterns and provide actionable insight for the design of robust and resilient multi-agent networks. Extensive simulations validate the theoretical results and demonstrate the effectiveness of our framework.