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