A receding-horizon (RH) optimal control scheme for a discrete-time nonlinear dynamic system is presented. A nonquadratic cost function is considered, and constraints are imposed on both the state and control vectors. Two main contributions are reported. The first consists in deriving a stabilizing regulator by adding a proper terminal penalty function to the process cost. The control vector is generated by means of a feedback control law computed off line instead of computing it on line, as is done for existing RH regulators. The off-line computation is performed by approximating the RH regulator by means of a multilayer feedforward neural network (this is the second contribution of the paper). Bounds to this approximation are established. Simulation results show the effectiveness of the proposed approach.