We tackle the problem of a set of agents achieving resilient consensus in the presence of attacked agents. We present a discrete-time reputation-based consensus algorithm for synchronous and asynchronous networks by developing a local strategy where, at each time, each agent assigns a reputation (between zero and one) to each neighbor. The reputation is then used to weigh the neighbors' values in the update of its state. Under mild assumptions, we show that: (i) the proposed method converges exponentially to the consensus of the regular agents; (ii) if a regular agent identifies a neighbor as an attacked node, then it is indeed an attacked node; (iii) if the consensus value of the normal nodes differs from that of any of the attacked nodes' values, then the reputation that a regular agent assigns to the attacked neighbors goes to zero. Further, we extend our method to achieve resilience in the scenarios where there are noisy nodes, dynamic networks and stochastic node selection. Finally, we illustrate our algorithm with several examples, and we delineate some attacking scenarios that can be dealt by the current proposal but not by the state-of-the-art approaches.

中文翻译：

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一种用于同步或异步通信的基于离散时间声誉的弹性共识算法

我们解决了一组代理在存在被攻击代理的情况下达成弹性共识的问题。我们通过开发本地策略为同步和异步网络提出了一种基于离散时间声誉的共识算法，其中每个代理每次都为每个邻居分配一个声誉（介于 0 和 1 之间）。然后在邻居的状态更新中使用声誉来衡量邻居的价值。在温和的假设下，我们表明：（i）所提出的方法以指数方式收敛到常规代理的共识；(ii) 如果常规代理将邻居识别为被攻击节点，那么它确实是被攻击节点；(iii) 如果正常节点的共识值与任何被攻击节点的值不同，则常规代理分配给被攻击邻居的声誉为零。此外，我们扩展了我们的方法以在存在噪声节点、动态网络和随机节点选择的场景中实现弹性。最后，我们用几个例子来说明我们的算法，并描述了一些可以由当前提议处理但不能由最先进方法处理的攻击场景。