论文标题
线性结构描述系统的最小可控性问题
Minimal controllability problems on linear structural descriptor systems
论文作者
论文摘要
我们考虑线性结构描述符系统上的最小可控性问题（MCP）。我们解决了确定最小输入节点数量的两个问题，以使描述符系统在结构上可以控制。我们表明，用于结构描述系统的MCP0可以在多项式时间内解决。这与典型的结构线性时间不变（LTI）系统的现有结果相同。但是，由于现有结果的派生技术不能用于描述符系统，因此结果的推导是大大差异。相反，我们使用dulmage- mendelsohn分解。此外，我们证明MCP1的结果与常规LTI系统的结果不同。实际上，用于描述符系统的MCP1是一个NP硬性问题，而LTI系统的MCP1可以在多项式时间内求解。
We consider minimal controllability problems (MCPs) on linear structural descriptor systems. We address two problems of determining the minimum number of input nodes such that a descriptor system is structurally controllable. We show that MCP0 for structural descriptor systems can be solved in polynomial time. This is the same as the existing results on typical structural linear time invariant (LTI) systems. However, the derivation of the result is considerably different because the derivation technique of the existing result cannot be used for descriptor systems. Instead, we use the Dulmage--Mendelsohn decomposition. Moreover, we prove that the results for MCP1 are different from those for usual LTI systems. In fact, MCP1 for descriptor systems is an NP-hard problem, while MCP1 for LTI systems can be solved in polynomial time.
