This work deals with the analysis and protocol design problems of finite-time consensus for multi-agent systems on signed and directed networks. A new distributed protocol with two reciprocal fractional power feedbacks of local consensus error has been proposed to remove the influence of initial states on the consensus time. By introducing a well-structured Lyapunov function, the technical difficulty arising from the asymmetrical Laplacian matrices of directed graphs is circumvented. Furthermore, it is shown that the feasibility of this proposed protocol can be extended to directed graphs with a spanning tree by mathematical induction method. The upper bounds of the finite-time periods are given under the circumstances of directed networks with a spanning tree apart from the strongly-connected ones. This new protocol is then extended to the application of finite-time bipartite formation control of multi-agent systems. Simulations and experiments of bipartite formation of multiple nano-quadcopters are implemented to prove the validity and practicability of this new protocol. In the experiment, a novel fuzzy logic is also introduced to realize the group collision avoidance of all nano-quadcopters.

这项工作解决了有向和有向网络上的多智能体系统的有限时间共识的分析和协议设计问题。提出了一种新的分布式协议，该协议具有两个局部共识误差的倒数分数功率反馈，以消除初始状态对共识时间的影响。通过引入结构良好的Lyapunov函数，可以避免由有向图的不对称Laplacian矩阵引起的技术难题。此外，证明了该提议协议的可行性可以通过数学归纳方法扩展到具有生成树的有向图。有限时间段的上限是在有向树且与强连接的树分开的有向网络的情况下给出的。然后，此新协议扩展到多智能体系统的有限时间二方形成控制的应用。进行了多个纳米quadcopters的两方形成的仿真和实验，以证明该新协议的有效性和实用性。在实验中，还引入了一种新颖的模糊逻辑来实现所有纳米四旋翼飞行器的群撞避免。