Average Consensus over Directed Networks in Open Multi-Agent Systems with Acknowledgement Feedback

TL;DR

This paper proposes a robust ratio consensus algorithm for directed open multi-agent systems that maintains average consensus despite frequent agent arrivals and departures, using acknowledgement feedback and stability properties.

Contribution

It introduces a novel OPENRC algorithm that ensures convergence in dynamic, unbalanced directed networks with agent churn, a significant advancement over existing methods.

Findings

The OPENRC algorithm maintains the sum of states during stable periods.

The algorithm converges under persistent network variations.

Simulation results demonstrate robustness to agent arrivals and departures.

Abstract

In this paper, we address the distributed average consensus problem over directed networks in open multi-agent systems (OMAS), where the stability of the network is disrupted by frequent agent arrivals and departures, leading to a time-varying average consensus target. To tackle this challenge, we introduce a novel ratio consensus algorithm (OPENRC) based on acknowledgement feedback, designed to be robust to agent arrivals and departures, as well as to unbalanced directed network topologies. We demonstrate that when all active agents execute the OPENRC algorithm, the sum of their state variables remains constant during quiescent epochs when the network remains unchanged. By assuming eventual convergence during such quiescent periods following persistent variations in system composition and size, we prove the convergence of the OPENRC algorithm using column-stochasticity and mass-preservation properties. Finally, we apply and evaluate our proposed algorithm in a simulated environment, where agents are departing from and arriving in the network to highlight its resilience against changes in the network size and topology.