Prescribed-Time Formation Tracking Control for Underactuated USVs with Prescribed Performance

This article proposes a prescribed-time formation tracking control scheme for USVs with prescribed performance constraints to address the issue of multiple underactuated USV formation tracking control with external environmental disturbances and input saturation. Initially, a prescribed-time extended state observer was constructed, capable of promptly estimating and compensating for speed and external disturbances within a certain timeframe. Additionally, a unique performance function was developed, enabling the performance function to converge to a predetermined accuracy within a specified time, while allowing for flexible adjustment of the performance constraint shape by parameter modification. Furthermore, a prescribed-time formation control algorithm was developed by combining graph theory and dynamic surface control, enabling the formation error to converge within preset performance constraints at a specified period of T=10 s. It was proved that all signals in the closed-loop system are uniform, ultimately bounded by Lyapunov stability theory and the formation tracking errors display prescribed-time stability. Finally, the efficacy and superiority of the designed control scheme were evaluated by constructing numerical simulations.