Bipartite formation control of second-order multi-agent systems with antagonistic interactions under dynamic event-triggered adaptive schemes

This article examines the adaptive leader-following bipartite formation (LBF) of second-order nonlinear multi-agent systems (MASs) with antagonistic interactions over a directed signed graph. To save the scarce communication resources efficiently, a novel distributed controller is designed for the LBF of the MASs, where a dynamic event-triggered (DET) control protocol with dynamic parameters is proposed. Meanwhile, the optimal control gains for realizing adaptive bipartite formation are obtained in accordance with the designed adaptive updating laws. By employing the DET mechanism and the Lyapunov functionals in conjunction, sufficient criteria for the adaptive LBF of the second-order MASs with antagonistic interactions and a directed signed graph are obtained. Furthermore, it has been demonstrated that Zeno phenomenon doesn't exist. Finally, the efficacy of the theoretical outcomes and the control protocol is validated through a numerical simulation.