Partial Resilient Leader-Follower Consensus in Time-Varying Graphs

2025-10-01

AI Summary

Existing approaches to leader-follower consensus in time-varying graphs with a bounded number of adversarial nodes rely on global strong robustness conditions; when these conditions fail, system behavior remains uncharacterized. Method: We introduce the notion of *partial consensus*, enabling a subset of normal followers to reliably track the leader’s state even under insufficient topological robustness. We propose a distributed algorithm—Bootstrap Percolation–Mean Subsequence Reduced (BP-MSR)—that leverages only local neighbor information to achieve resilient state tracking. Contribution/Results: This work provides, for the first time, provably resilient consensus guarantees for individual followers under arbitrary time-varying topologies. Simulations demonstrate that our method ensures consensus among a nontrivial subset of non-adversarial nodes in scenarios where standard resilient algorithms fail, thereby significantly enhancing system fault tolerance.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Adversarial Learning & Robustness
• Multiagent Systems: Adversarial Agents

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

This work studies resilient leader-follower consensus with a bounded number of adversaries. Existing approaches typically require robustness conditions of the entire network to guarantee resilient consensus. However, the behavior of such systems when these conditions are not fully met remains unexplored. To address this gap, we introduce the notion of partial leader-follower consensus, in which a subset of non-adversarial followers successfully tracks the leader's reference state despite insufficient robustness. We propose a novel distributed algorithm - the Bootstrap Percolation and Mean Subsequence Reduced (BP-MSR) algorithm - and establish sufficient conditions for individual followers to achieve consensus via the BP-MSR algorithm in arbitrary time-varying graphs. We validate our findings through simulations, demonstrating that our method guarantees partial leader-follower consensus, even when standard resilient consensus algorithms fail.

Problem

• Studying resilient leader-follower consensus with bounded adversaries
• Exploring consensus when network robustness conditions are unmet
• Achieving partial consensus via novel BP-MSR algorithm

Innovation

• BP-MSR algorithm enables partial consensus in adversarial networks
• Bootstrap Percolation and Mean Subsequence Reduced method introduced
• Achieves consensus in arbitrary time-varying graphs with adversaries