Sufficient conditions and limitations of equivalent partition in multiagent controllability  

作　　者：Junhao GUO Zhijian JI Yungang LIU 

机构地区：[1]Shandong Key Laboratory of Industrial Control Technology,Institute of Complexity Science,College of Automation,Qingdao University,Qingdao 266071,China [2]School of Control Science and Engineering,Shandong University,Jinan 250061,China

出　　处：《Science China(Information Sciences)》2022年第3期148-162,共15页中国科学（信息科学）（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 61873136,62033007, 61873146, 61703237);Taishan Scholars Climbing Program of Shandong Province and Taishan Scholar Project of Shandong Province of China (Grant No. ts20190930)。

摘　　要：The emergence of the graphical characterization of multiagent controllability has raised several issues concerning how to directly establish controllability from topology structures. Arguably, one of the most serious challenges to this research field is the means through which equivalent partition, which plays an important role in graphical characterization, obtains sufficient controllability conditions;hence, how equivalent partition influences controllability has garnered considerable attention. This article specifically focuses on the sufficient conditions and limitations of equivalent partition in multiagent controllability. We provide two sufficient conditions:(i) the absence of the system matrix’s eigenvectors that make the equation formed by the eigenvalues and eigenvectors hold and(ii) the addition of leaders by reducing the same number of followers. The first condition particularly exhibits a relation between two apparently unrelated parts: Tao’s equation and controllability. We further propose a necessary and sufficient condition for controllability under n-node graphs(n 5) by taking advantage of iso-neighbor nodes, and analyze the resulting difficulties when n is greater than 5. Immediate corollaries of our results are obtained. Finally, we reveal the limitation of equivalent partition in controllability analysis. Several constructive examples demonstrate our results.

关 键 词：multiagent system CONTROLLABILITY equivalent partition Tao’s equation graph theory 

分 类 号：O157.5[理学—数学] TP13[理学—基础数学]