Wang Lin, Wang Xiaofan, Chen Guanrong
Department of Automation, Shanghai Jiao Tong University, Ministry of Education, Shanghai, People's Republic of China
Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai, People's Republic of China.
Philos Trans A Math Phys Eng Sci. 2017 Mar 6;375(2088). doi: 10.1098/rsta.2016.0215.
In this paper, the state controllability of networked higher-dimensional linear time-invariant dynamical systems is considered, where communications are performed through one-dimensional connections. The influences on the controllability of such a networked system are investigated, which come from a combination of network topology, node-system dynamics, external control inputs and inner interactions. Particularly, necessary and sufficient conditions are presented for the controllability of the network with a general topology, as well as for some special settings such as cycles and chains, which show that the observability of the node system is necessary in general and the controllability of the node system is necessary for chains but not necessary for cycles. Moreover, two examples are constructed to illustrate that uncontrollable node systems can be assembled to a controllable networked system, while controllable node systems may lead to uncontrollable systems even for the cycle topology.This article is part of the themed issue 'Horizons of cybernetical physics'.
本文考虑了通过一维连接进行通信的网络化高维线性时不变动力系统的状态可控性。研究了网络拓扑、节点系统动力学、外部控制输入和内部相互作用的组合对这种网络化系统可控性的影响。特别地，给出了具有一般拓扑结构的网络以及一些特殊情形（如循环和链）可控性的充要条件，这些条件表明一般情况下节点系统的可观测性是必要的，对于链而言节点系统的可控性是必要的，而对于循环则不是必要的。此外，构建了两个例子来说明不可控的节点系统可以组装成一个可控的网络化系统，而即使对于循环拓扑结构，可控的节点系统也可能导致不可控的系统。本文是主题为“控制论物理学的前沿”特刊的一部分。
