论文标题
结构化网络的可扩展可控性分析
Scalable controllability analysis of structured networks
论文作者
论文摘要
本文涉及结构化网络的强大结构可控性。结构化网络是结构化系统（称为节点系统）的家族，通过结构化互连定律互连。节点系统及其结构化互连定律由模式矩阵给出。结果表明，当且仅当关联的结构化系统为时，结构化网络在结构上是可以控制的。通常，该结构化系统将具有很大的状态空间维度，因此现有用于验证强结构可控性的测试是无法探讨的。本文的主要结果规定了这个问题。 We show that controllability can be tested by replacing the original network by a new network in which all original node systems have been replaced by (auxiliary) node systems with state space dimensions either 1 or 2. Hence, controllability of the original network can be verified by testing controllability of a structured system with state space dimension at most twice the number of node systems, regardless of the state space dimensions of the original node systems.
This paper deals with strong structural controllability of structured networks. A structured network is a family of structured systems (called node systems) that are interconnected by means of a structured interconnection law. The node systems and their structured interconnection law are given by pattern matrices. It is shown that a structured network is strongly structurally controllable if and only if an associated structured system is. This structured system will in general have a very large state space dimension, and therefore existing tests for verifying strong structural controllability are not tractable. The main result of this paper circumvents this problem. We show that controllability can be tested by replacing the original network by a new network in which all original node systems have been replaced by (auxiliary) node systems with state space dimensions either 1 or 2. Hence, controllability of the original network can be verified by testing controllability of a structured system with state space dimension at most twice the number of node systems, regardless of the state space dimensions of the original node systems.
