In this paper, we present a novel method to drive a nonlinear system to adesired state, with limited a priori knowledge of its dynamic model: localdynamics at a single point and the bounds on the rate of change of thesedynamics. This method synthesizes control actions by utilizing locally learneddynamics along a trajectory, based on data available up to that moment, andknown proxy dynamics, which can generate an underapproximation of the unknownsystem's true reachable set. An important benefit to the contributions of thispaper is the lack of knowledge needed to execute the presented control method.We establish sufficient conditions to ensure that a controlled trajectoryreaches a small neighborhood of any provably reachable state within a shorttime horizon, with precision dependent on the tunable parameters of theseconditions.