Positive edge consensus of multiagent systems on directed graphs
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摘要: 现有针对多智能体系统的正连边一致性问题的研究，主要集中在无向图或强连通的有向图上。将其扩展到包含生成树的有向网络，由于包含生成树的有向网络的拉普拉斯矩阵可能为复数，分析较为困难。利用正系统理论和图论给出连边系统在包含生成树的有向网络下实现正一致性的充要条件。随后对结果进一步优化，通过改进拉普拉斯矩阵特征值的界，得到只涉及节点网络边数量的充分条件。求解Riccati不等式并提出一种半正定规划算法获得该解，最后通过数值仿真验证所得结果的有效性。Abstract: Most of the existing literature on the problem of positive edge consensus of multi-agent systems has mainly focused on undirected graphs or strongly connected directed graphs. To extend it to the directed networks containing spanning trees, since the Laplacian matrix of a directed network containing spanning trees may be complex, its analysis may become very difficult. Using positive system theory and graph theory, the necessary and sufficient conditions for edge system to achieve positive consensus under a directed network containing spanning trees were given. The results were further optimized by improving the bounds on the eigenvalues of the Laplace matrix, sufficient conditions involving only the number of edge number of the nodal network were obtained. Riccati inequality was solved and a semidefinite programming algorithm was developed to obtain the solution. Finally, the validity of the obtained results was verified by numerical simulation.
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Key words:
- multi-agent systems /
- directed spanning tree /
- positive edge consensus
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图 1 有向网络下节点图和线图的转化
Figure 1. Transformation of node graph and line graph under directed network
图 2 包含生成树的节点图和线图的转化
Figure 2. Transformation of node graph and line graph containing spanning trees
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