Fast Output Consensus Tracking of Heterogeneous Multi-Agent Systems Under Directed Graphs via a Fixed-Time Control Strategy

The brief is concerned with the fast output consensus tracking problem of heterogeneous multi-agent systems (MASs) under the digraph with a directed spanning tree. A novel fixed-time control protocol is proposed within the hierarchical framework, which not only endows a feature of faster convergency but also offers a more flexible estimation on the settling time comparing with asymptotic and finite-time protocols. Within the developed protocol, the challenge and complexity caused by heterogeneities of agents' dynamics and generalities of communication topologies can be fairly handled by recasting the fixed-time output consensus tracking problem into the problems of cooperative fixed-time estimation and local fixed-time tracking, separately. In upper layer, an elaborate potential function is designed to construct the fixed-time dynamic cooperative compensator to realize fast estimation of leader's states. In lower layer, based on the implicit Lyapunov function approach, a local fixed-time tracking controller is designed for each agent to track the compensator's states. Based on the incorporation of above two layers, each agent can track leader's output within a fixed time.