Bipartite flocking control for multi-agent systems with switching topologies and time delays under coopetition interactions

This paper investigates the bipartite flocking behavior of multi-agent systems with coopetition interactions, where communications between agents are described by signed digraphs. The scenario with switching topologies due to the movement of agents, and time delays caused by the limited data transmission capability, is considered comprehensively. Nonlinear weight functions are designed to describe the relationship between the communication distance of agents and the coopetition degree in real biological networks. A distributed update rule based on the neighbors' information and the designed weight functions is proposed. By the aid of the graph theory and sub-stochastic matrix properties, the effectiveness of the proposed update rule is proved theoretically, and the algebraic conditions for achieving the bipartite flocking behavior are obtained. Finally, the theoretical results are verified by numerical simulations.