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This note deals with the problem of fast implementation of nonlinear model predictive control using approximated control laws. At first, accuracy properties of a generic approximated controller κ̂ are introduced together with their influence on closed loop stability and performance. Then, exploiting such results, it is shown how Set Membership (SM) function approximation theory can be systematically employed to improve the accuracy performance of κ̂. The resulting controller, given by the sum of κ̂ with a SM approximating function, satisfies the above--mentioned properties even if they are not met by κ̂ alone. A nonlinear oscillator example shows the effectiveness of the proposed methodology.