A note on the fixed-time bipartite flocking for nonlinear multi-agent systems

This work focuses on the fixed-time bipartite flocking control problem for multi-agent systems. By employing the structurally balanced signed graph theory and a fixed-time stability theorem, we can prove that all individuals can be partitioned into two disjoint clusters within a fixed time and they move to opposite directions with the same velocity. We find that the settling time merely depends on the parameters and network connectivity. Moreover, the parameters, network connectivity and the initial states have an important influence on the diameter of each disjoint cluster. The results are novel, which are firstly illustrated by both theoretical analysis and numerical simulations.