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This study proposes an adaptive non‐singular integral terminal sliding mode control (ANITSMC) scheme for trajectory tracking of autonomous underwater vehicles (AUVs) with dynamic uncertainties and time‐varying external disturbances. The ANITSMC is first proposed for a first‐order uncertain non‐linear dynamic system to eliminate the singularity problem in conventional terminal sliding mode control (TSMC) and avoid the requirement of the bound information of the lumped system uncertainty. The time taken to reach the equilibrium point from any initial error is guaranteed to be finite. The proposed ANITSMC is then applied to trajectory tracking control of AUVs. It guarantees that the velocity tracking errors locally converge to zero in finite time and after that the position tracking errors locally converge to zero exponentially. The designed ANITSMC of AUVs avoids the requirement of the prior knowledge of the …