Distributed Event-Triggered Fixed-Time Leader–Follower Formation Tracking Control of Multiple Underwater Vehicles Based on an Adaptive Fixed-Time Observer

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.