论文标题
多代理形成控制中的双重四基矩阵
Dual Quaternion Matrices in Multi-Agent Formation Control
论文作者
论文摘要
与相互可见性图相关的三种双重四基因矩阵，即相对构型邻接矩阵，对数邻接矩阵和相对扭曲邻接矩阵，在多区域形成控制中起重要作用。在本文中，我们研究了它们的属性和应用。我们表明，相对构型邻接矩阵和对数邻接矩阵都是Hermitian矩阵，因此具有非常好的光谱属性。我们介绍了双季化laplacian矩阵，并证明了用于研究双重四基因laplacian矩阵的特性的正方形双季型遗传矩阵的gershgorin型定理。讨论了双重四元基质矩阵在形成控制中的作用。
Three kinds of dual quaternion matrices associated with the mutual visibility graph, namely the relative configuration adjacency matrix, the logarithm adjacency matrix and the relative twist adjacency matrix, play important roles in multi-agent formation control. In this paper, we study their properties and applications. We show that the relative configuration adjacency matrix and the logarithm adjacency matrix are all Hermitian matrices, and thus have very nice spectral properties. We introduce dual quaternion Laplacian matrices, and prove a Gershgorin-type theorem for square dual quaternion Hermitian matrices, for studying properties of dual quaternion Laplacian matrices. The role of the dual quaternion Laplacian matrices in formation control is discussed.
