This paper addresses the prescribed-time (PT) bounded consensus tracking problem for high-order nonlinear multi-agent systems subject to actuator faults, system uncertainties, and unmatched disturbances under directed communication topologies. A sufficient condition for PT bounded stability is established by introducing a smooth and bounded time-varying scaling function, which avoids singular time-varying scaling gains in the resulting control design. Based on this condition, an adaptive neural network-based control protocol is developed within a backstepping framework to approximate unknown nonlinear dynamics. To enhance implementability, a finite-time differentiator is incorporated to circumvent the explosion of complexity problem, while an adaptive fault compensation mechanism is constructed to address actuator effectiveness loss and bias faults. Rigorous Lyapunov analysis demonstrates that all closed-loop signals remain bounded and the consensus tracking errors converge to a small neighborhood of the origin within a user-specified time. Finally, simulation results are provided to illustrate the feasibility of the proposed approach and the bounded closed-loop behavior under the considered actuator-fault scenarios.
Zhao et al. (Mon,) studied this question.