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MAS Consensus and Delay Limits Under Delayed Output Feedback

机译：延迟输出反馈下的MAS共识和延迟极限

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In this technical note, we study the consensus problem for discrete-time multi-agent systems over an undirected, fixed network communication graph, focusing on the robustness of consensus with respect to communication delay. We assume that the agents' input is subject to a constant albeit possibly unknown time delay, and is generated by a distributed dynamic output feedback control protocol. Drawing upon concepts and techniques from robust control, notably those concerning gain margin optimization and analytic interpolation, we derive explicit, closed-form conditions for general linear agents to achieve consensus. Our results display an explicit dependence of the consensus condition on the delay value as well as on the agent's unstable poles and non-minimum phase zeros, showing that delayed communication between agents will generally hinder consensus and impose restrictions on the network topology. We also show that a lower bound on the maximal delay allowable for consensus can be computed by a simple line search method.
机译：在此技术说明中，我们研究了无向，固定网络通信图上离散时间多主体系统的共识问题，重点是针对通信延迟达成共识的鲁棒性。我们假设代理的输入受到恒定的影响，尽管可能是未知的时间延迟，并且是由分布式动态输出反馈控制协议生成的。借鉴鲁棒控制的概念和技术，特别是涉及增益裕量优化和解析插值的概念和技术，我们得出了一般线性代理达成共识的显式封闭形式条件。我们的结果显示了共识条件对延迟值以及代理的不稳定极点和非最小相位零的显着依赖，这表明代理之间的延迟通信通常会阻碍共识，并对网络拓扑施加限制。我们还表明，可以通过简单的行搜索方法来计算共识允许的最大延迟的下限。

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