  This paper addresses the distributed prescribed-time leader-following
consensus problem for a class of high-order multi-agent systems (MASs) with
perturbed nonlinear agents dynamics and where the topology of the network
contains a directed spanning tree, with the leader as the root. Prescribed-time
consensus means that an agreement state of the MAS is achieved in a preset
time, introduced as a parameter of the control law, and this constant settling
time is achieved independently of the agents' initial state. The proposed
control method exhibits three main advantages: first, to our best knowledge, it
is the first time that prescribed-time convergence in a consensus problem is
achieved for agents with high-order nonlinear dynamics, using a robust
leader-following protocol, which allows an effective rejection of matched
disturbances in the agents' model. Second, the proposed controller provides
control signals of lower magnitude than existing approaches. Third, the
proposed consensus protocol does not have parameters to be adjusted depending
on the connectivity of the considered communication graph.
