Fixed-Time Consensus Based on a Fractional Adaptive Gain for Multi-Agent Systems.

In this article, a fractional adaptive gain is adopted to solve fixed-time consensus problem. Both leaderless and leader-following consensus based on different communication topologies are considered and the stability is proved by Lyapunov analysis. With the help of the adaptive gain, the settling time is related to the first zero of a Mittag-Leffler function. Theoretical analysis demonstrates that the proposed protocol has smoother control input since the fractional gain is adaptive, and it is more robust since it is not time-based. The results of the simulation show that the convergence rate is faster and both the initial and the magnitude of the control input are smaller under our protocols. In addition, the basis of selecting parameters in the proposed method is also presented, which is consistent with the simulation results.