On Adversary Robust Consensus protocols through joint-agent interactions
David Angeli, Sabato Manfredi
TL;DR
This work addresses robust consensus in multi-agent networks containing faulty or malicious agents by introducing a generalized framework of monotone joint-agent interactions and modeling the network as a Petri Net. The authors derive a topological, necessary-and-sufficient condition called robust consensuability, based on controlled siphons, under which healthy agents converge to a common value $\bar{x}$ despite bounded disturbances from faults $x_F(\cdot)$. They provide a nonlinear, continuous-time dynamical system formulation, prove convergence using invariance arguments and omega-limit analysis, and illustrate the approach with grid-based examples and a comparison to ARC-P protocols. The results bridge nonlinear consensus with discrete-event system theory, offering structural tools for designing robust, topology-aware consensus protocols while highlighting limitations against fully Byzantine threats that require future study.
Abstract
A generalized family of Adversary Robust Consensus protocols is proposed and analyzed. These are distributed algorithms for multi-agents systems seeking to agree on a common value of a shared variable, even in the presence of faulty or malicious agents which are updating their local state according to the protocol rules. In particular, we adopt monotone joint-agent interactions, a very general mechanism for processing locally available information and allowing cross-comparisons between state-values of multiple agents simultaneously. The salient features of the proposed class of algorithms are abstracted as a Petri Net and convergence criteria for the resulting time evolutions formulated by employing structural invariants of the net.