This paper studies the bipartite consensus problem for a network of wave PDEs. The interactions among participating individuals may be antagonistic characterized by a signed digraph. Two distributed algorithms consisting of boundary sensing of the agents’ states are proposed for the disturbance-free and disturbed cases, respectively. Then Lyapunov function is constructed to assure bipartite consensus of the agents. Moreover, the relationship between control gain and communication topology is also explicitly revealed. Using the tool from semigroup theory, the property of well-posedness of the underlying systems is guaranteed. Finally, numerical examples are given to support the proposed setup.

本文研究了波动PDE网络的两方共识问题。参与的个体之间的相互作用可以是对抗性的，其特征在于签名的有向图。针对无扰动情况和受扰动情况，分别提出了两种由代理状态边界检测组成的分布式算法。然后构造Lyapunov函数以确保代理的两方共识。此外，还明确揭示了控制增益与通信拓扑之间的关系。使用半群理论的工具，可以保证底层系统的适定性。最后，给出了数值示例来支持所提出的设置。