More than a decade ago Fliess and co-workers [1], [2], [3] proposed model-free control as a possible answer to the inherent difficulties in controlling non-linear systems. Their key insight was that by using a sufficiently high sampling rate we can use a simple linear model for control purposes thereby trivializing controller design. In this paper, we provide a variation of model-free control for which it is possible to formally prove the existence of a sufficiently high sampling rate ensuring that controllers solving output regulation and tracking problems for the approximate linear model also solve the same problems for the true and unknown nonlinear model. This is verified experimentally on the bipedal robot AMBER-3M.