Predefined-time tracking problem for nonlinear multi-agent systems subject to bounded disturbances

This paper investigates the predefined-time leader-following consensus problem for a class of nonlinear multi-agent systems subject to bounded disturbances. A class of fixed-time stable dynamical systems is thoroughly analysed, and the exact expression of the least upper bound of the settling time is rigorously derived. Building upon this foundation, a novel class of predefined-time stable systems is systematically constructed by incorporating the predefined time as a core parameter. Leveraging this theoretical framework, a non-smooth control protocol is designed for nonlinear leader-following multi-agent systems affected by bounded disturbances. Theoretical analysis proves that under the proposed protocol, all followers can accurately synchronise with the leader within the user-specified predefined time. Finally, comparative numerical simulations are conducted to fully verify the effectiveness and robustness of the proposed control strategy.