This paper investigates the cooperative formation control problem in unmanned surface vehicles (USVs) with prescribed performance constraints under complex marine conditions including external disturbances, model uncertainties, actuator faults, and input saturation. A novel fault-tolerant control (FTC) algorithm is developed by integrating cooperative learning neural networks (NNs), distributed disturbance observers, and the backstepping technique. Specifically, the learning NNs adaptively approximate system uncertainties, and the learned weight information is shared among vehicles to enhance cooperative cognition. Additionally, an auxiliary dynamic system and an actuator configuration matrix are designed to compensate for input saturation and propeller failures. Theoretical analysis based on the Lyapunov method proves that all signals in the closed-loop system are bounded, and the formation tracking errors strictly remain within the predefined transient and steady-state performance bounds. Finally, simulation experiments involving a group of four USVs validate the proposed algorithm. The results demonstrate that the USVs can rapidly converge to and maintain the desired quadrilateral formation shape despite time-varying disturbances and actuator efficiency loss. Furthermore, comparative simulation results indicate that the proposed cooperative learning FTC scheme significantly reduces velocity tracking error oscillations compared to traditional non-learning methods, explicitly verifying its superior robustness and fault-tolerant capabilities.
Zhang et al. (2026) studied this question.