Eigenvector-based characterization for hierarchical multi-agent dynamical systems with low rank interconnection
Eigenvector-based characterization for hierarchical multi-agent dynamical systems with low rank interconnection
复制标题
DOI：
10.1109/cca.2010.5611133
复制
发表时间：
2010-10
期刊：
影响因子：
--
通讯作者：
Daisuke Tsubakino;S. Hara
中科院分区：
文献类型：
--
作者：
Daisuke Tsubakino;S. Hara
本文基于一个新的特征互连概念，研究了具有低秩互连的层次多智能体动力系统。特征向量在我们的框架中起着重要的作用。我们首先定义的特征互连矩阵的秩一的情况下。然后，我们给出了具有秩为1的特征互连矩阵的分层互连的特征值分布。所得到的特征值分布具有显式的参数依赖性，其结果允许我们有选择地放置特征值。从而为分层互连结构的设计提供了有用的知识。这个概念自然地推广到秩二的情况下，得到了类似的结果特征值分布。这些结果完全包含了以前的研究作为特例。此外，我们的特征具有直接扩展到更高秩的情况下的潜力。最后，我们给出了一个数值例子，其中的分层互连结构的设计基于我们的结果。
In this paper, we investigate hierarchical multi-agent dynamical systems with low rank interconnection based on a new concept of eigen-interconnection. The eigenvector plays an important role in our framework. We first define the eigen-interconnection matrix for the rank one case. Then, we show eigenvalue distribution of a hierarchical interconnection with rank one eigen-interconnection matrix. The obtained eigenvalue distribution has explicit parameter dependency and the result allows us to place the eigenvalue selectively. Thus it gives useful knowledge to design hierarchical interconnection structure. This concept is naturally extended to the rank two case and a similar result for eigenvalue distribution is obtained. Those results completely include the previous researches as special cases. Furthermore, our characterization has a potential of straightforward extension to the higher rank cases. Finally, we show a numerical example where a hierarchical interconnection structure is designed based on our result.