Predefined-time bipartite tracking consensus for second-order multi-agent systems with cooperative and antagonistic networks

This paper addresses the predefined-time bipartite tracking problem for second-order Multi-Agent Systems (MASs) with undirected signed topologies. A group of observers, which can estimate the state tracking errors for each follower in a pre-specified time, is proposed based on the time-varying function. In order to deal with the uncertainties caused by the unknown disturbances and the unknown input signal of the leader, we propose a predefined-time distributed control protocol based on the sliding mode control method. In addition, an auxiliary dynamic sliding variable is designed to reduce system chattering. We theoretically prove that the two control protocols can drive the state trajectories of each follower to reach the corresponding sliding surface within a specified time, and finally ensure that the prescribed-time bipartite tracking consensus is achieved for the MASs. Simulations are provided to verify the proposed schemes, and the simulation results further confirm the superiority of the adaptive control protocol.