报告题目：Weighted Directed Graph and Formation Control

报 告 人：祁力群教授（杭州电子科技大学）

报告时间：2024年9月23日  10:00-11:30

报告地点：格物楼数学研究中心528报告厅

报告摘要：

We first study the multi-agent formation control problem in a directed graph. The relative configurations are expressed by unit dual quaternions (UDQs). We call such a weighted directed graph a unit dual quaternion weighted directed graph (UDQWDG). We show that a desired relative configuration scheme is reasonable in a UDQWDG if and only if for any cycle in this directed graph is egual to 1. We then show that a desired relative configuration scheme in a directed connected graph is reasonable if and only if the dual quaternion Laplacian is similar to the unweighted Laplacisn of the directed graph. Then for a reasonable desired relative configuration scheme, we build the relationship between the desired formation and the eigenvector corresponding to the zero eigenvalue.

报告人简介：

祁力群教授，香港理工大学应用数学荣休教授，杭州电子科技大学教授。曾任教于清华大学、澳大利亚新南威尔士大学、香港城市大学和香港理工大学，他建立了半光滑牛顿方法的超线性收敛理论，和光滑化牛顿方法的全局收敛理论。祁教授的论文广为应用，在2003-2010与2018-2022年度被列为世界高被引数学家，祁力群教授在2005年提出高階张量特征值，並继而形成高階张量谱理论，在医疗工程、数据分析、量子物理、超图谱理论、液晶研究等。祁力群在多个国际杂志担任主编或编委。