Second-order multi-agent consistency based on edge event triggering

To solve the consistency problem of second-order multi-agent systems, this paper proposes a control strategy based on edge event triggering, and adds a dynamic threshold to reduce the number of events triggered. When the trigger condition is met, the agent transmits information only to the other agent on the adjacent side, avoiding sending information to all neighboring agents, which reduces the waste of system resources. The introduction of auxiliary dynamic variables allows the threshold to be dynamically adjusted to avoid the problem of events being triggered continuously. Lyapunov stability theory is used to prove that the control system based on edge event triggering is asymptotically stable without Zeno behavior, and the effectiveness of the control strategy is verified by simulation. In order to prove that the control protocol proposed in this paper can indeed reduce the number of trigger events, the paper also compares with other literatures, and concludes that using the trigger function in this paper can indeed reduce the number of trigger events, and achieve consistent time invariability, which proves the advantages of the protocol in this paper.