Formation control over antagonistic networks

In this paper, a network of agents have antagonistic interactions and a new formation control problem is mathematically formulated and analyzed with the help of signed graph theory. Firstly, a formation control is designed for each agent in the antagonistic network. Then a sufficient and necessary condition is presented to ensure that the agents in the allied groups achieve their own desired formations with an opposite direction to the rivals over undirected/directed networks. Finally, some numerical examples are provided to illustrate the effectiveness of the antagonistic formation controls.