In this paper, the finite-time coordination behavior of multiple Euler-Lagrange systems in cooperation-competition networks is investigated, where the coupling weights can be either positive or negative. Then, two auxiliary variables about the information exchange among agents are designed, and the finite-time distributed protocol is proposed based on the auxiliary variables and the property of the Euler-Lagrange system. By combining the approach of adding a power integrator with the homogeneous domination method, it is shown that finite-time bipartite consensus can be achieved if the cooperation-competition network is structurally balanced and the parameters of the distributed protocol are chosen appropriately; otherwise, finite-time distributed stabilization can be achieved. Furthermore, from the perspective of network decomposition, the finite-time coordination behavior is further considered, and some sufficient conditions about the cooperation subnetwork and the competition subnetwork are obtained. As an extension, finite-time coordination behavior only with partial state information of the neighbors is discussed, and some similar results are obtained. Finally, four numerical examples are shown for illustration.

中文翻译：

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合作竞争网络中多个Euler__agrange系统的有限时间协调行为


本文研究了合作竞争网络中多个欧拉-拉格朗日系统的有限时间协调行为，其中耦合权值可以是正的，也可以是负的。然后，设计了两个关于Agent间信息交换的辅助变量，并根据辅助变量和Euler-Lagrange系统的性质提出了有限时间分布式协议。将添加功率积分器的方法与同质支配方法相结合，证明了在合作竞争网络结构平衡、分布式协议参数选择适当的情况下，可以实现有限时间双方共识；否则，可以实现有限时间分布式稳定。此外，从网络分解的角度，进一步考虑有限时间协调行为，得到了合作子网络和竞争子网络的一些充分条件。作为扩展，讨论了仅利用邻居部分状态信息的有限时间协调行为，并得到了一些类似的结果。最后，给出了四个数值例子进行说明。