This paper studies the edge controllability of signed networks, where the dynamics taking place on edges and the interaction type over each edge can be cooperative or antagonistic. First, the edge controllable subspace is studied quantitatively from the graph-theoretic perspective. And the lower and upper bounds for the dimension of edge controllable subspace are derived, respectively. Second, the relationship between edge controllability and vertex controllability is analyzed. We prove that the controllability of the edge dynamics is equivalent to that of the vertex dynamics when the communication graph is structurally unbalanced. Furthermore, the edge structural controllability of signed networks is investigated, and a graph-theoretic necessary and sufficient condition for edge structural controllability is presented. Finally, we demonstrate possible applications of our theoretical results to the traffic flow control of urban traffic networks.

本文研究了符号网络的边可控性，其中边上发生的动态和每条边上的交互类型可以是合作的或对抗的。首先，从图论的角度对边可控子空间进行了定量研究。并分别推导了边缘可控子空间维数的下界和上界。其次，分析了边缘可控性和顶点可控性之间的关系。我们证明当通信图在结构上不平衡时，边动力学的可控性等同于顶点动力学的可控性。此外，研究了带符号网络的边结构可控性，并提出了边结构可控性的图论充分必要条件。最后，