Research On Bipartite Consistency Of Multi-agent Systems Based On Adaptive Event Triggering Mechanis

The research on bipartite consensus of multi-agent systems is one of the hot issues in the field of control in recent years.This paper mainly studies the bipartite consensus problem of multi-agent systems under adaptive event-triggered mechanism,including the following contents:1.The research background of consensus for multi-agent systems,the research statuses of bipartite consensus,finite-time consensus and matrix weighted consensus are introduced.Basic theoretical knowledge such as algebraic graph theory is provided.2.For general linear multi-agent systems,a distributed adaptive dynamic event-triggered control protocol is proposed,and the dynamic threshold can guarantee fewer events.Under the structurally balanced communication topology,sufficient conditions are given to ensure the realization of the asymptotic bipartite consensus of the system,and it is proved that each adaptive coupling weight converges to a finite steady-state value.It is proved by contradiction that there is no Zeno behavior in the system under the given conditions.3.For first-order nonlinear multi-agent systems,under the assumption that the control input of the dynamic leader is unknown and bounded,static and dynamic distributed fast finite-time leader-following bipartite consensus protocols are proposed,respectively.Under the structurally balanced communication topology,sufficient conditions are given to guarantee the fast finite-time leader-following bipartite consensus.The introduced adaptive coupling weights can effectively avoid the dependence on the global information of systems.4.For the first-order multi-agent systems with matrix-weighted communication topology,the edge-based and node-based adaptive event-triggered bipartite consensus protocols are proposed,respectively,and the designed event-triggered function is related to the spectrum of the weight matrices.Under the structurally balanced communication topology,sufficient conditions are given to ensure that the system achieves asymptotic bipartite consensus.It is proved by contradiction that there is no Zeno behavior in the system under the given conditions.