<p>This paper presents an adaptive control strategy designed for strict-feedback nonlinear systems affected by input saturation, output hysteresis, and external disturbances. The handling of output hysteresis phenomena employs an inverse model, while the uncertainty due to time-varying control gain from output hysteresis is managed using the Nussbaum-type function technique. To tackle non-smooth input saturation nonlinearity, a smooth, non-affine function approximates the saturation signal, and multi-dimensional Taylor network (MTN) is utilized for managing unknown nonlinear functions. Building on these methods, an adaptive controller based on MTN is developed using the backstepping technique and the approximation capabilities of MTN. Stability analysis of the closed-loop system is conducted through Lyapunov stability theory, ensuring semi-globally uniformly ultimately bounded (SGUUB) closed-loop system behavior and convergence of the tracking error to a small neighborhood around the origin. Simulation examples are provided to demonstrate the effectiveness and practicality of the proposed control methodology.</p>