AI 中文总结
针对异构移动智能体网络，提出用邻接矩阵主导特征向量替代Fiedler向量的A-Fiedler方法，提升分布式估计鲁棒性，为分布式网络控制提供更简单路径。
AI 中文摘要
我们考虑由不受控的任务智能体和可控制的通信智能体组成的异构移动智能体网络，目标是在任务智能体移动时在线重新定位通信智能体。由于基于吞吐量的目标通常不适用于实时控制，谱图度量（如代数连通性）常被用作代理目标。然而，控制代数连通性依赖于图拉普拉斯矩阵中对应第二小特征值的特征向量（即Fiedler向量），其分布式估计需要无限多的通信轮次才能收敛。本研究中，我们将该Fiedler梯度控制器识别为局部交互规则和图嵌入组件的结构分解，表明可使用比Fiedler向量更易分布式估计的替代嵌入。作为一个特定实例，我们提出A-Fiedler，它用邻接矩阵的主导特征向量（通常用作节点到潜在几何的图嵌入）替代Fiedler嵌入，该表示在局部通信约束下更适合分布式实现。我们将A-Fiedler与经典Fiedler梯度控制器进行评估，结果显示在无通信约束时网络性能相当，且在分布式估计下鲁棒性更好。例如，在相同通信轮次下，Fiedler梯度甚至可能收敛到不连通配置，而我们的方案保持性能。我们认为，本研究的贡献为分布式网络控制提供了更简单的路径。
英文摘要
We consider a heterogeneous mobile-agent network composed of uncontrolled task agents and controllable communication agents. The objective is to reposition communication agents online as task agents move. Since throughput-based objectives are generally unsuitable for real-time control, spectral graph metrics such as algebraic connectivity are commonly adopted as surrogate objectives. However, controlling algebraic connectivity relies on the eigenvector corresponding to the second-smallest eigenvalue of a graph's Laplacian matrix (i.e., the Fiedler vector), whose distributed estimation requires an unbounded number of communication rounds to converge. In this work, we identify a structural decomposition of this Fiedler-gradient controller into a local interaction rule and a graph embedding component, suggesting the use of alternative embeddings that are easier to estimate distributively than the Fiedler vector. As a particular instance, we propose A-Fiedler, which replaces the Fiedler embedding with the dominant eigenvector of the adjacency matrix, commonly used as a graph embedding of nodes into a latent geometry. This representation is more naturally suited for distributed implementation under local communication constraints. We evaluate A-Fiedler against the classical Fiedler-gradient controller. Results show comparable network performance in the absence of communication constraints and improved robustness under distributed estimation. For instance, under the same number of communication rounds, the Fielder-gradient may even converge to disconnected configurations whereas our proposition maintains performance. We believe our contribution provides a simpler path toward distributed network control.
