Global Fixed-Time Prescribed Performance Control Using Exponential Shift Function for Multiple Unmanned Surface Vehicles Formation

This paper primarily investigates the control method for prescribed performance constraints in globally fixed-time underactuated formations of multi-unmanned surface vehicles (USVs). A novel exponential shift function is originally proposed to address the non-global convergence issue of state tracking errors in the initial phase of the multi-USV system, which is influenced by initial conditions. A stabilization method for azimuth error formation is proposed using the global fixedtime prescribed performance approach, enabling the multi-USV formation to achieve the desired configuration within a predetermined fixed time. Additionally, by integrating dynamic surface control techniques, a global fixed-time prescribed performance yaw controller is designed to ensure both steady-state and transient performance of the multi-USV system. Theoretical analysis demonstrates that each dynamic tracking error within the multiUSV system converges to a presupposed residual set within a fixed time frame. Simulation results validate the effectiveness of the proposed control methodology.