Adaptive Predefined-Time Formation Control of USVs via a Novel Distributed Super-Twisting-Like Estimator

In this article, an adaptive distributed predefined-time and bounded (PTB) sliding mode controller based on a novel super-twisting-like estimator is proposed for the formation control problem of underactuated uncrewed surface vehicles (USVs) subject to unknown disturbances. To leverage the advantages of the super-twisting estimator and achieve ultimate PTB stability in the formation control system, a novel distributed predefined-time super-twisting-like estimator is first proposed. This estimator achieves real-time estimation of the leader's position and velocity within a predefined-time by collecting the neighboring USVs' estimates of the leader's position and velocity through switching interaction topologies, and it does not require the leader's acceleration information. Next, an improved nonsingular PTB sliding surface is designed. By integrating this sliding surface with adaptive control techniques, a distributed PTB sliding mode formation controller is designed for underactuated USVs subject to unknown disturbances. Finally, the PTB stability of the formation control system is rigorously proven. Numerical simulations of both fixed and time-varying formations validate the effectiveness and robustness of the proposed method.