提出新型网络拓扑，让多智能体系统突破平均值共识限制。
On Robustness of Consensus over Pseudo-Undirected Path Graphs
- 用可带负权的伪无向路径图实现双向通信但权重不对称
- 在连通条件下仍能达成稳定共识，且结果可超出初始状态范围
- 适合需要灵活共识目标的协同拦截等场景
多智能体系统中的一致性通常基于无向或有向通信图研究。无向图保证信息对称，收敛于初始值平均；有向图允许非对称，但依赖根节点影响。两者均限制了可达成的一致性值和网络鲁棒性。本文提出一种理论框架，用于一类称为伪无向图的网络拓扑，该类拓扑保持节点间双向连接，但边权重可不相等，包括在有界条件下允许负权重。由此产生的拉普拉斯矩阵一般非对称，但在连通性假设下仍能保证一致性，拓展了解空间，使系统可达到初始状态凸包之外的稳定共识值。我们推导了伪无向路径图中负权重的可接受边界，并展示了在同时拦截移动目标中的应用。
原文摘要 · Abstract (English)
Consensus over networked agents is typically studied using undirected or directed communication graphs. Undirected graphs enforce symmetry in information exchange, leading to convergence to the average of initial states, while directed graphs permit asymmetry but make consensus dependent on root nodes and their influence. Both paradigms impose inherent restrictions on achievable consensus values and network robustness. This paper introduces a theoretical framework for achieving consensus over a class of network topologies, termed pseudo-undirected graphs, which retains bidirectional connectivity between node pairs but allows the corresponding edge weights to differ, including the possibility of negative values under bounded conditions. The resulting Laplacian is generally non-symmetric, yet it guarantees consensus under connectivity assumptions, to expand the solution space, which enables the system to achieve a stable consensus value that can lie outside the convex hull of the initial state set. We derive admissibility bounds for negative weights for a pseudo-undirected path graph, and show an application in the simultaneous interception of a moving target.
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