We study a multi-agent resilient consensus problem, where some agents are of the Byzantine type and try to prevent the normal ones from reaching consensus. In our setting, normal agents communicate with each other asynchronously over multi-hop relay channels with delays. To solve this asynchronous Byzantine consensus problem, we develop the multi-hop weighted mean subsequence reduced (MW-MSR) algorithm. The main contribution is that we characterize a tight graph condition for our algorithm to achieve Byzantine consensus, which is expressed in the novel notion of strictly robust graphs. We show that the multi-hop communication is effective for enhancing the network's resilience against Byzantine agents. As a result, we also obtain novel conditions for resilient consensus under the malicious attack model, which are tighter than those known in the literature. Furthermore, the proposed algorithm can be viewed as a generalization of the conventional flooding-based algorithms, with less computational complexity. Lastly, we provide numerical examples to show the effectiveness of the proposed algorithm.

翻译：我们研究一个多智能体弹性共识问题，其中部分智能体为拜占庭类型，试图阻止正常智能体达成共识。在本场景中，正常智能体通过具有延迟的多跳中继信道异步通信。为解决该异步拜占庭共识问题，我们提出了多跳加权均值子序列缩减（MW-MSR）算法。主要贡献在于：我们刻画了该算法实现拜占庭共识所需的严格图条件，该条件以新颖的"严格鲁棒图"概念表述。研究表明，多跳通信可有效增强网络对拜占庭智能体的抵御能力。由此，我们还在恶意攻击模型下获得了比现有文献更严格的弹性共识新条件。此外，所提算法可视为传统洪泛算法的泛化形式，具有更低计算复杂度。最后，通过数值算例验证了算法的有效性。