| Summary: | This article 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.
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