AI 中文总结
研究开放多智能体系统非均匀缩放编队控制问题，开发分布式协议调整拉普拉斯矩阵部分权重，能在动态拓扑变化下保留期望编队谱，具有更稀疏传感图、无需预定义层次结构和支持领导者重新分配等优势，经理论分析和模拟验证有效。
AI 中文摘要
非均匀缩放控制使多智能体编队能够通过智能体间交互沿不同坐标轴独立压缩或拉伸来调整形状，在复杂环境中具有高灵活性。其基本思想是将期望编队形状编码为矩阵值拉普拉斯的核。然而在开放多智能体系统中，智能体数量、边数量和领导者选择的变化会动态改变拉普拉斯，破坏所需谱特性。本文开发分布式协议在任意维空间中策略性调整拉普拉斯矩阵部分权重以进行编队控制。通过实施该协议，在包括智能体加入、边添加、智能体离开和边移除等动态拓扑变化下可保留期望编队谱，且任意一对智能体都可作为领导者。与现有拓扑变化下仿射编队控制的拉普拉斯设计方法不同，该方法需要更稀疏的传感图，避免预定义父子层次结构并支持领导者重新分配。通过理论分析和数值模拟验证了所提协议的有效性。
英文摘要
Non-uniform scaling control enables a multi-agent formation to adjust its shape by compressing or stretching independently along different coordinate axes through inter-agent interactions, offering high flexibility in complex environments. The fundamental idea is encoding the desired formation shape as the kernel of a matrix-valued Laplacian. In open multi-agent systems, however, changes in number of agents, number of edges, and leader selection dynamically alter this Laplacian, destroying the required spectral properties: positive semidefiniteness, correct kernel, and positive definiteness of the follower block (we summarize these properties as the formation spectrum). In this paper, we develop distributed protocols to strategically adjust partial weights of the Laplacian matrix for formation control in arbitrary dimensional space. By implementing the protocols, the desired formation spectrum can be preserved under dynamic topology changes including agent joining, edge addition, agent leaving, and edge removal, while any pair of agents can serve as leaders. Unlike existing Laplacian design methods for affine formation control under topology changes, the proposed approach requires a sparser sensing graph, avoids a predefined parent-child hierarchical structure, and supports leader reassignment. The effectiveness of the proposed protocols is validated through both theoretical analysis and numerical simulations.
