This work deals with the analysis and protocol design problems of the prescribed-time interval bipartite consensus of multi-agent systems on signed and directed graphs. A new distributed protocol with hybrid constant and time-varying feedbacks of local signed error is proposed, whose consensus time period is independent of the specific topology among agents and initial states of all agents. By introducing a series of well-structured Lyapunov functions, the technical difficulties arising from the asymmetrical Laplacian matrices of directed graphs are circumvented. The effectiveness of this prescribed-time protocol for multi-agent systems on signed digraphs with a spanning tree is proven both on structurally balanced digraphs and structurally unbalanced ones with a positive root subgraph. An illustrative simulation example and a prescribed-time bipartite formation experiment on a swarm of nano-quadcopters are implemented to show the validity and practicability of these proposed protocols.

中文翻译：

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有向图上多智能体系统的分布式规定时间区间二部共识：理论与实验

这项工作解决了在有向图和有向图上多智能体系统的规定时间间隔二分共识的分析和协议设计问题。提出了一种新的分布式协议，该协议具有混合的常数和时变的局部符号错误反馈，其一致的时间周期与代理之间的特定拓扑和所有代理的初始状态无关。通过引入一系列结构良好的Lyapunov函数，可以避免有向图的非对称拉普拉斯矩阵带来的技术难题。具有结构树的有向有向图的多智能体系统上，这种规定时间协议对于多智能体系统的有效性已在结构平衡的有向图和具有正根子图的非平衡的有向图上得到了证明。