Formation Control of Multiagent Networks: Cooperative and Antagonistic Interactions

This article studies the formation control problem of second-order multiagent networks, in which cooperative and antagonistic interactions of the agents spontaneously coexist in the communication process. Based on the convex analysis theory, several convex polytopes that do not require some kinds of system constraints are constructed in the presence of these interactions. Then, the matrix perturbation theory and some mathematical techniques are utilized to analyze these convex polytopes. The obtained results show that the agents with cooperative interactions monotonously converge to their own specified formation shape while maintaining the desired relative position of the other agents with antagonistic interactions. Subsequently, two numerical examples are presented to illustrate the obtained results.