This paper describes the optimal tuning for the output limits of the power system stabilizer (PSS), which can improve the system damping performance immediately following a large disturbance. The non-smooth nonlinear parameters such as the saturation limits of the PSS cannot be tuned by the conventional methods based on linear approaches. To implement the systematic optimal tuning for the output limits of the PSS, a feedforward neural network (FFNN) is applied to the hybrid system model based on the differential-algebraic- impulsive-switched (DAIS) structure. The FFNN is firstly designed to identify the trajectory sensitivities obtained from the DAIS structure. Thereafter, it estimates the second-order derivatives of an objective function J, which is used during iterations of optimization process. The performance of the optimal output limits tuned by the proposed method is evaluated by applying a large disturbance to a power system.