A Novel Class of Distributed Fixed-Time Consensus Protocols for Second-Order Nonlinear and Disturbed Multi-Agent Systems

The fixed-time consensus problem is considered in this paper for second-order multi-agent systems (MASs) with inherent nonlinear dynamics and disturbances under a detail-balanced network in both leaderless and leader-following cases. The fixed-time consensus means that MASs reach consensus in finite time and the settling time is uniformly bounded with respect to initial states. Based on the bi-limit homogeneity method, a novel class of distributed consensus protocols are proposed to handle different models. First, when there is no disturbance, some new continuous distributed control protocols are presented which make a group of agents reach consensus within a fixed time for both leaderless and leader-following MASs. Then, if there exist disturbances, the sliding mode control method is utilized to design discontinuous consensus protocols for both leaderless and leader-following MASs, respectively. Finally, several simulation examples are given to illustrate the effectiveness of the theoretical results.