Fixed-Time Bipartite Tracking Consensus of Heterogeneous Multi-Agent Systems Subject to Input Disturbances

This paper investigates the fixed-time bipartite tracking consensus problem for heterogeneous multi-agent systems (HMASs) in a directed signed network. The HMASs consist of a fractional-order leader and first-order followers which subject to input disturbances. Not only the different dynamic characteristics, but also the directional communication networks among heterogeneous agents, which increase the difficulty of controller design. According to the Lyapunov stability theory and graph theory, a more compact fixed-time distributed protocol is proposed, which rejects bounded disturbances by simply specifying a sufficiently large gain coefficient for the nonlinear control input. Under the designed protocol, followers can achieve bipartite consensus tracking for leader agent within a preset settling time, which is independent of the initial values of agents. Finally, several simulation tests are presented to verify the effectiveness of the proposed controller.