Objective This paper investigates the multi-objective collaborative encirclement and tracking control problem for underactuated unmanned surface vehicles (USVs) under unknown time-varying environmental disturbances. A decoupled control method for position and velocity is proposed based on the prescribed-time control approach.

Method In the position control layer, considering the real-time changes in the positions of multiple targets and the underactuated nature of the USVs, a prescribed-time cooperative encirclement tracking guidance law is designed. This law enables the USVs to track a convex combination of multiple targets, with a time-varying scaling of the encirclement. In the velocity control layer, a prescribed-time sliding mode encirclement control law is developed to track the desired velocity signal output by the guidance law. To mitigate the impact of unknown time-varying disturbances on the control system, the prescribed-time theory is incorporated into the weight update law of the Radial Basis Function Neural Network (RBFNN). A prescribed-time RBFNN disturbance estimator is introduced to estimate and compensate for the disturbances experienced by the system. The Lyapunov stability theory is employed to analyze and prove that the proposed control method ensures the prescribed-time stability of the system.

Results Simulation results demonstrate that the proposed method can achieve the convergence of position tracking errors, velocity tracking errors, and disturbance estimation errors to zero within the prescribed time. The disturbance estimation method reduces the longitudinal velocity integral absolute error and the yaw rate integral absolute error of the USV formation by 13.55% and 24.46%, respectively. Compared with the fixed-time control method, the prescribed-time control method reduces the integral error of position tracking by 8.5%, improves convergence speed by 57.89%, and reduces the longitudinal velocity integral absolute error and the yaw rate integral absolute error of the USV formation by 29.06% and 62.9%, respectively.

Conclusion In conclusion, the proposed method effectively stabilizes the state of the USV formation multi-target tracking control system within the prescribed time, enhancing both the convergence speed and accuracy of the system's control errors. It also offers notable advantages in estimating unknown time-varying environmental disturbances and improving the system's dynamic performance.