Abstract <p>This paper presents an event-triggered adaptive neural network zeta-backstepping control method for a class of nonlinear systems with unknown nonlinearities and external disturbances. A self-adjusting damping ratio strategy is introduced to dynamically regulate the damping ratio, enabling faster convergence through a lower damping ratio during the initial response phase. As the system approaches the steady state, the damping ratio is increased to effectively suppress potential overshoot and enhance closed-loop stability. A radial basis function neural network, trained online using a gradient descent algorithm, is employed to estimate and compensate for system uncertainties and external disturbances, thereby enhancing the robustness and tracking performance of the controller. Furthermore, to alleviate the signal transmission burden, a novel hyperbolic secant function-based event-triggered mechanism is proposed, which significantly reduces the controller update frequency without compromising control performance. Based on the second-order stability criterion, it is rigorously proven that the tracking error of the nonlinear system achieves practical stability under the dynamically adjusted damping ratio, while Zeno behavior is avoided. Finally, experimental results obtained on a quadrotor hover platform demonstrate the effectiveness and superiority of the proposed method. Compared with three representative gain configurations of conventional adaptive neural network backstepping controllers across four representative operating conditions, the proposed method reduces the average settling time and the average maximum overshoot by approximately 64% and 70%, respectively.</p> Graphical abstract <p></p>