具有领导者的高阶线性多运动体系统的群智汇集趋同  

Cluster consensus for leader-following high-order linear multiagent systems

作　　者：马翠芹 杜梅 赵云波 MA CuiQin;DU Mei;ZHAO YunBo(School of Mathematical Sciences,Qufiu Normal University,Qufu 273165,China;Department of Automation,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]曲阜师范大学数学科学学院,曲阜273165 [2]中国科学技术大学自动化系,合肥230026

出　　处：《中国科学：技术科学》2023年第2期307-316,共10页Scientia Sinica(Technologica)

基　　金：国家自然科学基金(批准号:61973183、62173317);山东省自然科学基金(编号:ZR2019MF041);山东省高等学校青创科技计划(编号:2019KJI007)资助项目。

摘　　要：本文研究了具有领导者的高阶线性多运动体系统的群智汇集趋同问题.利用运动体与其邻居的信息,分别为跟随者设计了状态反馈型和输出反馈型控制协议,并利用矩阵Riccati代数方程、矩阵分析等工具,给出了系统实现领导-跟随者群智汇集趋同的充分条件.研究表明,当领导者和跟随者所组成的多运动体系统的通信拓扑交互平衡并且存在一棵生成树时,只要合理地选取满足条件的控制增益,系统在所给出的控制协议作用下可以实现领导-跟随者群智汇集趋同.特别地,当为跟随者设计输出反馈型控制协议时,借助误差系统可以将领导-跟随者群智汇集趋同问题转化为静态输出反馈问题.当系统的输入输出矩阵满足一定的秩条件时,系统在所设计的输出反馈型控制协议作用下可以实现领导-跟随者群智汇集趋同.Cluster consensus for leader-following high-order linear multiagent systems(MASs)is investigated.Based on the information of an agent and its neighbors,state feedback and output feedback control protocols are designed for each follower,respectively.Sufficient conditions for leader-following cluster consensus are given using tools from the algebraic Riccati equation and matrix analysis.It is shown that if the communication topology of an MAS composed of the leader and followers is interactively balanced and contains a spanning tree,the MAS can achieve leader-following cluster consensus under the proposed control protocols by properly selecting control gains.Particularly,it is found that the leader-following cluster consensus problem based on the output feedback protocol can be transformed into a static output feedback problem using an error system.If the input and output matrices of a follower satisfy a certain rank condition,the MAS can achieve leader-following cluster consensus under the designed output feedback control protocol.

关 键 词：多运动体系统 群智汇集趋同 领导-跟随者 加权符号图 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]