This paper proposes an optimal adaptive super-twisting sliding-mode control (OASTSMC) via adaptive dynamic programming (ADP) to achieve high precision-positioning for linear stage considering the uncertain nonlinear dynamics of the permanent-magnet synchronous motor (PMSM) servo drive actuator. First, the position of the linear-stage is stabilized through super-twisting sliding-mode controller (STSMC). However, the control performance may be destroyed due to parameter uncertainties, friction and backlash nonlinearities of the ball-screw and external disturbances. Therefore, to improve the robustness and to achieve high precision-positioning, an OASTSMC is designed to achieve this purpose. The OASTSMC incorporates a STSMC, a FLNN identifier and an optimal feedback controller. The STSMC is adopted to reduce the chattering, the FLNN identifier is developed for the approximation of uncertain nonlinear dynamics online and the infinite horizon optimal control is developed using a critic NN and ADP to facilitate the online solution of the Hamilton-Jacobi-Bellman (HJB) equation. The dynamic behavior of linear-stage using the OASTSMC assures the stability of the closed-loop and guarantees the optimal performance for the overall system. The validation of the proposed control scheme is carried out to verify the efficacy of the OASTSMC approach through experimental analysis. The experimental results confirm good dynamic performance of linear-stage.