A composite control scheme that deals with longitudinal dynamics problems of the missiles suffering from matched and unmatched disturbances is proposed.First,a Super-Twisting Disturbance Observer (STDO) is used to estimate the unknown disturbance,and an Integral Sliding Mode Controller (ISMC) is designed to compensate for the input disturbance.Subsequently,the differential game theory and Adaptive Dynamic Programming (ADP) algorithm are combined to approximate the optimal control by constructing a single critic Neural Network (NN) to counteract the unmatched disturbance online.The stability of closed-loop system and the convergence of the weights of critic network are proved by Lyapunov stability theory.Finally, the effectiveness of the proposed scheme is proved by designing a longitudinal dynamics model of a missile.