Edge controllability of signed networks

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.(c) 2022 Published by Elsevier Ltd.