Event-Triggered Consensus Of Time-Varying Multi-Agent Systems

In the past few decades, multi-agent systems has extensive concerned by the research of scholars. The consensus of multi-agent systems is one of the key issues and has a widespread application, such as formation, posture positioning, flocking control,rendezvous, etc.Due to the limitation of communication resources,a kind of discontinuous control has been proposed. First,rational trigger condition should be designed? Then,the system need update its control and send its state to its neighboring agents when the trigger condition is satisfied. Otherwise, the system keep previous control. This control is event-triggered control. This paper apply the event-triggered control to address the consensus problem of linear time-varying multi-agent systems and the consensus problem of nonlinear time-varying multi-agent systems.In section 1, we establish an event-triggered consensus scheme for a general class of linear time-varying multi-agent systems over networks. The consensus error can converge to zero exponentially and no Zeno behavior occurs. Then we apply the methods to design the consensus control for a group of identical linear time-varying multi-agent systems over a network having a spanning tree. We further employ the proposed event-triggered consensus scheme to solve the event-triggered distributed cooperative adaptive identification problem for a group of static linear parameterized systems. If the regression matrices of all systems satisfy the cooperative PE condition developed recently and the network is undirected and connected, the consensus error can converge to zero exponentially and no Zeno behavior occurs. Finally, two simulation examples illustrate the effectiveness of the event-triggered scheme proposed in this paper.In section 2, we propose the event-triggered consensus scheme for nonlinear time-varying systems over networks. Due to the system is nonlinear time-varying function and the interconnection function in systems is time-varying, we couldn't choose a suitable Lyapunov function for the analysis of consensus. Under some rational assumptions for nonlinear time-varying function, the consensus error can converge to zero exponentially and the Zeno behavior is excluded. Finally, a simulation example illustrates theeffectiveness of the event-triggered scheme proposed in this paper.