This paper considers max-consensus of a discrete-time multi-agent system (MAS) in directed random networks. Interactions among agents in the MAS are probabilistic and independent with each other. By using max-plus algebra and random theory, a sufficient and necessary condition is given for achieving max-consensus of the MAS. Moreover, we demonstrate that the max-consensus in four probabilistic senses (almost surely, in probability, expectation and mean square) is equivalent when expected graph is strongly connected. This ensures that max-consensus can be achieved in multi-agent systems even if random failures occur in the communication network, which is of practical importance in the fields of wireless sensor networks and distributed computing. A simulation example is presented to illustrate the effectiveness of theoretical results.

中文翻译：

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随机网络中多智能体系统的最大共识

本文考虑有向随机网络中离散时间多智能体系统（MAS）的最大共识。 MAS 中的代理之间的交互是概率性的并且彼此独立。利用最大加代数和随机理论，给出了实现 MAS 最大共识的充分必要条件。此外，我们证明，当预期图强连通时，四种概率意义上的最大共识（几乎可以肯定，概率、期望和均方）是等效的。这保证了即使通信网络发生随机故障，多智能体系统也能实现最大共识，这在无线传感器网络和分布式计算领域具有重要的实际意义。给出了一个仿真例子来说明理论结果的有效性。