Set membership function estimation methodologies are employed in the approximation of a given predictive control law. This is obtained via the evaluation of an approximating function with a desired level of accuracy, fulfilling input constraints and whose computational time is independent on the MPC control horizon. The effects of employing the approximated control law can be treated as an additive perturbation acting on the system. Sufficient conditions are obtained for the approximating function to guarantee closed loop stability, state constraint satisfaction and limited performance degradation, in terms of distance between the nominal and perturbed state trajectories. Then, as the control computation is simply reduced to the evaluation of a static non linear function, the computational time is significantly reduced leading to a fast implementation of the given predictive controller.