Distributed prescribed‐time leader‐following formation control for second‐order multi‐agent systems with mismatched disturbances

Abstract This article investigates the distributed prescribed‐time formation control problem for the second‐order multi‐agent systems (MASs) subject to matched and mismatched disturbances in time‐varying formation case. As a stepping stone, novel distributed estimators are first proposed to accurately estimate the position and velocity information of the leader within prescribed time. Subsequently, the nominal control protocol is presented for the MAS in the absence of the disturbances to deal with the time‐varying formation control problem, and the prescribed‐time stability of the system is guaranteed. For system subject to matched and mismatched disturbances, the observer‐based integral sliding mode formation control protocol is then presented such that the desired trajectories can be tracked and the desired patterns can be achieved within the prescribed settling time. By adopting the sinusoidal function to the control scheme, the singularity‐like problem is solved if there exist measurement errors in the agents. Finally, a numerical simulation example utilizing unmanned aerial vehicles modeled by Simscape and Solidworks is presented to show the efficiency of the proposed scheme.