Abstract In this paper, a finite-time extended state observer-based nonsingular fast terminal sliding mode control (NFTSMC) is proposed for the trajectory tracking of autonomous underwater vehicles (AUVs) with various hydrodynamic uncertainties and external disturbances. First, a proportional–integral velocity variable based third-order fast finite-time extended state observer is designed to estimate the lumped uncertainties and their first derivatives. The concepts of finite-time stability and a new proposition are utilized to prove the finite-time uniformly ultimately boundness of the proposed observer. Then, based on the disturbance estimation, an NFTSMC is developed for AUVs. The inverse tangent function and linear control term are used to provide robustness against estimation error and avoid chattering in the thrusters. The position and attitude trajectories are proved to be fast finite-time stable via the Lyapunov theorem. To verify the theoretical analysis, comparative numerical simulations are provided to demonstrate the effectiveness of the proposed control scheme.

中文翻译：

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基于有限时间扩展状态观测器的自主水下航行器非奇异快速终端滑模控制

摘要 本文提出了一种基于有限时间扩展状态观测器的非奇异快速终端滑模控制（NFTSMC），用于具有各种水动力不确定性和外部干扰的自主水下航行器（AUV）的轨迹跟踪。首先，设计了一个基于比例积分速度变量的三阶快速有限时间扩展状态观测器来估计集总不确定性及其一阶导数。利用有限时间稳定性的概念和一个新命题来证明所提出观测器的有限时间一致最终有界。然后，基于扰动估计，为 AUV 开发了 NFTSMC。反正切函数和线性控制项用于提供对估计误差的鲁棒性，并避免推进器中的抖动。通过李雅普诺夫定理证明了位置和姿态轨迹是快速有限时间稳定的。为了验证理论分析，提供了比较数值模拟来证明所提出的控制方案的有效性。