Model predictive control of nonlinear sampled-data systems is studied, with a particular focus on computational efficiency. In order to reduce the computational requirements associated with the solution of the continuous-time nonlinear system equations, the process is modelled by a set of linear models constructed by velocity-based linearization. The resulting quasi-linear models also simplify the estimation of the system state from the measured outputs. The on-line computational burden associated with the controller calculation is reduced by using a neural network function approximator to approximate the optimal model predictive control strategy. The accuracy of the neural network controller approximation which is required to ensure stability and performance is shown to be related to the fragility of the model predictive controller, which can be characterized in terms of an l(2)-induced norm defined for the closed-loop system. The proposed approach is applied to a simulated nonlinear pH neutralization process. (C) 2004 Elsevier Ltd. All rights reserved.