<p>Barrier function-based adaptive sliding mode control can guide the sliding variable into a predefined space in finite time; however, its final convergence set is fixed by the maximum disturbance limit and cannot be adjusted by the user. To address this limitation, this paper develops a final-set adjustable saturation-tolerant predefined space–time adaptive sliding mode control method for systems subject to actuator saturation and disturbance. By designing an auxiliary system with only a single tunable parameter to introduce the boundary saturation-tolerant index, the proposed method ensures that the final set is not only smaller than those of existing barrier function-based adaptive sliding mode control methods, but can also be flexibly adjusted through user-specified parameters and dynamically regulated according to the degree of input saturation. This characteristic enables the controller to ensure that the sliding variable reaches the adaptively adjusted saturation-tolerant space within the predefined time, even under input saturation. In addition, the user can preset the convergence space and time in advance unaffected by the initial condition and disturbance. Furthermore, the method alleviates excessive initial control gain estimation and avoids segmenting the control scheme. The stability and the adjustability of the final set of the method are rigorously proven. Simulations and experiments on a piezoelectric fast steering mirror show substantial reductions in the final set and root mean square error—reduced by 73.3% and 81.87% in simulation and at least 55.67% and 31.52% experimentally.</p>