Fast finite-time consensus strategy for multi-agent systems based on switching of different protocols

In multi-agent systems (MASs), the time to reach a consensus is an important factor in characterising system performance and control strategy. The linear protocol has a fast convergence rate when the initial error is large but slows significantly as the error decreases. Therefore, this paper combines the linear protocol with two finite-time protocols, and a switching strategy is designed to achieve fast finite-time consensus. First, when the connection topology is undirected, it is proved that the continuous finite-time consensus protocol is unnecessary, with the fastest convergence achieved by switching directly from the linear protocol to the discontinuous finite-time protocol. Two switching thresholds are provided. Subsequently, the results are extended to detail-balanced and leader-following graphs. Notably, in the leader-following case, the graph only needs to be connected without requiring strongly connected or detail-balanced. The proposed approach significantly reduces the time required for MAS consensus and eliminates the need for additional parameter calculations.