Combinatorics

Discrete mathematics

Graph

Directed graph

Topology (electrical circuits)

Digraph

Mathematics

Multi-agent system

Cartesian product

Betweenness centrality

Mathematical analysis

Artificial intelligence

Computer science

Network controllability

Centrality

Theoretical computer science

Applied mathematics

Controllability

Graph theory

Polynomial

IEEE Transactions on Control of Network Systems

In this article, the structural controllability of multiagent networks defined over directed signed graphs is investigated, where the agents are divided into leaders and followers, and only leaders are manipulated by the external control input directly. The communication digraph contains positive and negative edges, which represent cooperative and antagonistic interactions between agents, respectively. First, a graph-theoretic necessary and sufficient condition for structural controllability of multiagent networks is derived, that is, a multiagent network is structurally controllable if and only if the communication digraph is leader–follower connected. Next, the minimal controllability problem is studied. It is shown that the minimal controllability problem is solvable, and a method of polynomial complexity to accomplish minimal structural controllability is developed. In addition, the structural controllability of specified Cartesian product networks is discussed and a necessary and sufficient condition concerning the factor networks for the structural controllability is established. The application of the theoretical results is demonstrated by several practical examples.

Structural Controllability of Directed Signed Networks