Controllability Ensured Leader Group Selection on Signed Multiagent Networks

Leader–follower controllability on signed multiagent networks is investigated in this paper. Specifically, we consider a dynamic signed multiagent network, where the agents interact via neighbor-based Laplacian feedback and the network allows positive and negative edges to capture cooperative and competitive interactions among agents. The agents are classified as either leaders or followers, thus forming a leader–follower signed network. To enable full control of the leader–follower signed network, controllability ensured leader group selection approaches are investigated in this paper, that is, identifying a small subset of nodes in the signed network, such that the selected nodes are able to drive the network to a desired behavior, even in the presence of antagonistic interactions. In particular, graphical characterizations of the controllability of signed networks are first developed based on the investigation of the interaction between network topology and agent dynamics. Since signed path and cycle graphs are basic building blocks for a variety of networks, the developed topological characterizations are then exploited to develop leader selection methods for signed path and cycle graphs to ensure leader–follower controllability. Along with illustrative examples, heuristic algorithms are also developed showing how leader selection methods developed for path and cycle graphs can be potentially extended to more general signed networks. In contrast to existing results that mainly focus on unsigned networks, this paper characterizes controllability and develops leader selection methods for signed networks. In addition, the developed results are generic, in the sense that they are not only applicable to signed networks but also to unsigned networks, since unsigned networks are a particular case of signed networks that only contain positive edges.