This paper focuses on the fixed-time leader–follower formation control of multiple underwater vehicles (MUVs) in the presence of external disturbances. First, an adaptive fixed-time disturbance observer (AFxDO) is developed to deal with unknown time-varying environmental disturbances. The developed AFxDO guarantees the fixed-time convergence property of the disturbance observation error and no prior information on the external disturbances or their derivatives is required. Then, with the aid of the developed AFxDO, a distributed event-triggered fixed-time backstepping controller was developed to achieve the leader–follower formation tracking control of MUVs. To solve the “explosion of complexity” problem inherent in the conventional backstepping, a nonlinear filter is introduced to obtain the derivative of the virtual control law. Furthermore, to reduce the communication burden, the event-triggered mechanism is integrated into the formation tracking controller. The stability analysis shows that the closed-loop MUV system is practical fixed-time stable. Finally, simulation results demonstrate the effectiveness of the proposed scheme.

This paper proposes the wave peak frequency tracking methods based on the least squares identification algorithm. The wave disturbance model is transformed into an autoregressive moving average (ARMA) model and a recursive extended least squares (RELS) algorithm is derived to identify the model parameters by using the auxiliary model identification idea. Furthermore, a two-stage recursive extended least squares (2S-RELS) algorithm is presented to improve the convergence speed by using the hierarchical identification principle. A ship heading control system with the wave peak frequency tracker is built to evaluate the effectiveness of the proposed algorithms. Finally, simulation results show that the proposed algorithms can estimate the wave peak frequency accurately and the 2S-RELS algorithm can improve the convergence speed effectively.

This paper investigates the problem of trajectory tracking control of underactuated autonomous underwater vehicles (AUVs) with predefined time convergence. To this end, a predefined time nonlinear disturbance observer is designed with the aim of accurately estimating unknown external disturbances. This observer is capable of capturing the dynamic influences on the AUV in real time to support the subsequent control strategy. By setting the time parameters reasonably, the convergence time of the system can be set in advance, thus ensuring that the desired tracking effect is achieved within a specific time. In addition, a predefined time backstepping controller is designed for the problem of AUV trajectory tracking. Theoretical analysis shows that the upper limit of its convergence time is only determined by a constant, which simplifies the parameter tuning process and enhances the practicability compared with the existing finite/fixed time control methods. The effectiveness and superiority of the proposed method are verified through further simulation studies, which show that the control strategy has good trajectory tracking performance.