Adaptive event-triggered bipartite consensus control for multi-agent systems under signed digraphs

In this paper, the bipartite consensus problem is addressed via adaptive event-triggered control for multi-agent systems in directed communication networks, where cooperative and competitive interactions are considered simultaneously. Under a strongly connected digraph, a novel fully distributed control protocol is first put forward, which consists of an adaptive controller and two event-triggered mechanisms. The protocol is flexible and capable of achieving bipartite consensus without employing global information. Meanwhile, the Zeno behavior cannot occur by embedding Lp$$ {L}_p $$ functions in the event-triggered mechanisms. Furthermore, a general digraph with a spanning tree is investigated, and it is shown that the proposed protocol is still effective in bipartite consensus including the leader-follower one as a special case. It is worth noting that there is no need for the protocol to continuously update the controller, nor to maintain the uninterrupted communication with neighbors. Finally, the validity of the presented results is confirmed by simulations.