Resilience for Distributed Consensus With Constraints

Xuan Wang, Shaoshuai Mou, Shreyas Sundaram

Abstract: This article proposes a new approach that enables multiagent systems to achieve resilient constrained consensus in the presence of Byzantine attacks, in contrast to existing literature that is only applicable to unconstrained resilient consensus problems. The key enabler for our approach is a new device called a $(\gamma _{i},\alpha _{i})$-Resilient Convex Combination, which allows normal agents in the network to utilize their locally available information to automatically isolate the impact of the Byzantine agents. Such a resilient convex combination is computable through linear programming, whose complexity scales well with the size of the overall system. By applying this new device to multiagent systems, we introduce network and constraint redundancy conditions under which resilient constrained consensus can be achieved with an exponential convergence rate. We also provide insights on the design of a network such that the redundancy conditions are satisfied. Finally, numerical simulations and an example of safe multiagent learning are provided to demonstrate the effectiveness of the proposed results.

External IDs:dblp:journals/tac/WangMS25