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符号网络条件下扩散耦合多智能体系统的可控性分析

赵兰浩1,2,纪志坚1,2   

  1. 1.青岛大学自动化学院, 青岛 266071; 2.山东省工业 控制技术重点实验室,青岛 266071
  • 出版日期:2021-06-25 发布日期:2021-09-17

赵兰浩, 纪志坚. 符号网络条件下扩散耦合多智能体系统的可控性分析[J]. 系统科学与数学, 2021, 41(6): 1455-1466.

ZHAO Lanhao, JI Zhijian. Controllability Analysis of Diffusion Coupled Multi-Agent System Under Signed Networks[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(6): 1455-1466.

Controllability Analysis of Diffusion Coupled Multi-Agent System Under Signed Networks

ZHAO Lanhao1,2 ,JI Zhijian1,2   

  1. 1. School of Automation, Qingdao University, Qingdao 266071; 2. Shandong Key Laboratory of Industrial Control Technology, Qingdao 266071
  • Online:2021-06-25 Published:2021-09-17
针对符号网络条件下扩散耦合多智能体网络的可控 性进行了研究. 基于广义几乎等价划分的方法, 结合系统系数 矩阵的限制条件, 运用图理论, 给出了此时系统可控子空间维数 的上界, 并给出了系统可控的一个必要条件, 即系统可控时, 划 分中所有胞腔都是平凡的. 给出了一种用来计算最大领导者孤立广义几乎 等价划分的算法. 此外, 还证明了结构平衡条件下, 如果从同一个顶点 集中选择领导者, 则扩散耦合多智能体系统的可控性与对应的全正网络 的可控性是等价的, 而与系统系数矩阵的选取无关.
In this paper, the controllability of diffusion coupled multi-agent systems under signed networks is studied. Firstly, the upper bound of the controllable subspace of the system is given based on the generalized almost equitable partition and the restriction on the coefficient matrix of the system. Compared with the previous similar conclusions, the influence of the choice of coefficient matrix on the conclusion is discussed and a necessary condition for the controllability of the system is given: All the cells in the partition are trivial when the system is controllable. Secondly, an algorithm for computing the leader-isolated maximal generalized almost equitable partition is presented. In addition, it is proved that the controllability of the general linear diffusion coupled multi-agent system is equivalent to the controllability of the corresponding all positive network if leaders are selected from the same vertex set under the condition of structural balance, but independent of the selection of system coefficient matrix.
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