<p>In this paper, the problem of adaptive hierarchical non-singular terminal sliding mode control (NTSMC) for constrained under-actuated nonlinear systems with sensor faults is investigated under a dynamic event-triggered mechanism (ETM). Due to the existence of sensor faults, all the real state variables are unavailable. Based on the state variables actually measured by the sensor, an original system is transformed into an unconstrained system by a unified barrier function (UBF) to solve the problem of time-varying asymmetric state constraints. Subsequently, a hierarchical NTSMC technique is proposed to achieve finite-time convergence and improve robustness for the under-actuated systems. A robust adaptive fault accommodation controller is designed via involving neural networks, which can compensate the uncertainty and nonlinear dynamics caused by the fault without prior knowledge of the fault coefficient. Meanwhile, a dynamic ETM is used to reduce unnecessary information transmissions. According to the Lyapunov stability theory, it is strictly proved that all the signals of the closed-loop system are bounded. Finally, the effectiveness of the proposed control scheme is illustrated by simulation results of an overhead crane system.</p>