论文标题
双线性系统图表上的可控性和可访问性
Controllability and Accessibility on Graphs for Bilinear Systems over Lie Groups
论文作者
论文摘要
本文介绍了在特殊正交组，特殊线性组和一般线性组的双线性系统可控制性和可访问性的图形理论条件下，分别存在漂移项。这样的双线性系统自然会诱导两个相互作用图：一个来自漂移的图，另一个来自受控动力学。结果，鉴于经典的Lie代数等级条件，系统可控性或可访问性成为两个图的属性。我们建立了一种系统性的方式，将基础谎言代数中的谎言括号操作转换为删除或在漂移和受控交互图上的特定操作。结果，我们为此类双线性系统的可控性和可访问性建立了一系列图形条件，这些条件仅依赖于漂移和受控相互作用图的联合的连通性。我们提出了例子来说明既定结果的有效性，并表明所提出的条件实际上很紧张。
This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift terms. Such bilinear systems naturally induce two interaction graphs: one graph from the drift, and another from the controlled dynamics. As a result, the system controllability or accessibility becomes a property of the two graphs in view of the classical Lie algebra rank condition. We establish a systemic way of transforming the Lie bracket operations in the underlying Lie algebra, into specific operations of removing or creating links over the drift and controlled interaction graphs. As a result, we establish a series of graphical conditions for the controllability and accessibility of such bilinear systems, which rely only on the connectivity of the union of the drift and controlled interaction graphs. We present examples to illustrate the validity of the established results, and show that the proposed conditions are in fact considerably tight.
