Prescribed time adaptive periodic sliding mode control of unmanned surface vehicle cluster under singular disturbance

This paper proposes an adaptive prescribed-time periodic sliding mode control method to address the issue of singular disturbances in the rapid convergence of unmanned surface vehicle (USV) formation control. Firstly, preset performance ensures that the formation error of the closed-loop control system converges within a predefined allowable range. An adaptive control gain function is introduced to adjust the control gain in real-time according to the system state. Secondly, considering the unknown control direction, a periodic sliding mode method is proposed to maintain the robustness of the tracking project, and virtual signals and actual control laws are defined. Furthermore, this method ensures that the tracking error converges to zero within a user-defined time frame, regardless of the initial conditions. Simulation results demonstrate the effectiveness of this method, providing a new solution for the rapid convergence and stable control of unmanned surface vehicle formations.