Privacy-Preserving Resilient Vector Consensus

This paper studies privacy-preserving resilient vector consensus in multi-agent systems against faulty agents, where normal agents can achieve consensus within the convex hull of their initial states while protecting state vectors from being disclosed. Specifically, we consider a modification of an existing algorithm known as Approximate Distributed Robust Convergence Using Centerpoints (ADRC), i.e., Privacy-Preserving ADRC (PP-ADRC). Under PP-ADRC, each normal agent introduces multivariate Gaussian noise to its state during each iteration. We first provide sufficient conditions to ensure that all normal agents' states can achieve mean square convergence under PP-ADRC. Then, we analyze convergence accuracy from two perspectives, i.e., the Mahalanobis distance of the final value from its expectation and the Hausdorff distance-based alteration of the convex hull caused by noise when only partial dimensions are added with noise. Then, we employ concentrated geo-privacy to characterize privacy preservation and conduct a thorough comparison with differential privacy. Finally, numerical simulations demonstrate the theoretical results.