A discrete-time neural inverse optimal control is designed for a three-phase linear induction motor (LIM) in order to control its position. This controller is optimal in the sense that it minimises a cost functional. A recurrent high-order neural network, trained with the extended Kalman filter, is employed to obtain a mathematical model for the LIM with uncertainties. A super twisting-based state estimator provides an estimate of the unmeasurable state variables of the system. This control scheme is applied in real time in an LIM prototype which achieves trajectory tracking for a position reference.