This paper proposes a distributed algorithm for average consensus in a multi-agent system under a fixed bidirectional communication topology, in the presence of malicious agents (nodes) that may try to influence the average consensus outcome by manipulating their updates. The proposed algorithm converges asymptotically to the average of the initial values of the non-malicious nodes, which we refer to as the trustworthy average, as long as the underlying topology that describes the information exchange among the non-malicious nodes is connected. We first present a distributed iterative algorithm that assumes that each node receives (at each iteration or periodically) side information about the trustworthiness of the other nodes, and it uses such trust assessments to determine whether or not to incorporate messages received from its neighbors, as well as to make proper adjustments in its calculation depending on whether a previously trustworthy neighbor becomes untrustworthy or vice-versa. We show that, as long as the trust assessments for each non-malicious node eventually reflect correctly the status (malicious or non-malicious) of its neighboring nodes, the algorithm guarantees asymptotic convergence to the trustworthy average. We subsequently discuss how the proposed algorithm can be enhanced with functionality that enables each node to obtain trust assessments about its neighbors by utilizing information that it receives from its two-hop neighbors at infrequent, perhaps randomly chosen, time instants.

翻译：本文提出了一种分布式算法，用于在固定双向通信拓扑的多智能体系统中实现平均共识，同时存在可能通过操纵其更新来影响平均共识结果的恶意节点。所提出的算法渐近收敛于非恶意节点初始值的平均值，我们称之为可信平均值，前提是描述非恶意节点间信息交换的基础拓扑是连通的。我们首先提出一种分布式迭代算法，该算法假设每个节点（在每次迭代或周期性地）接收关于其他节点可信度的辅助信息，并利用这些信任评估来决定是否采纳来自其邻居的消息，以及根据先前可信的邻居变为不可信或反之的情况，在其计算中做出适当调整。我们证明，只要对每个非恶意节点的信任评估最终能正确反映其邻居节点的状态（恶意或非恶意），该算法就能保证渐近收敛到可信平均值。随后，我们讨论了如何通过功能增强所提出的算法，使每个节点能够利用从其二跳邻居在低频（可能随机选择）时刻接收的信息，获取关于其邻居的信任评估。