Fixed-Time Consensus of Multi-Agent Systems with Directed and Intermittent Communications

This paper proposes a new class of nonlinear protocols for fixed-time consensus in networked agents with directed and intermittent communications. First of all, based on the assumption of a common positive dwell time for all successful links, it is theoretically shown that the asymptotical consensus can be achieved if the interaction topology with some fixed length of time has a spanning tree. Then, if the length sum of time intervals, over which the directed interaction topology contains a spanning tree, is larger that a threshold value, which is independent of initial conditions, the system will solve a fixed-time consensus problem. Furthermore, in light of the mirror operation principle of graph theory, the proposed protocol is extended to solve the fixed-time consensus problem if a common positive dwell time for all active links is strongly connected without the detailed balanced condition. Finally, the effectiveness of the theoretical results is illustrated by simulation results.