Before revision:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics  , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists. This allows fora small bound on the tracking error when the trajectory is executed on the real system .
After revision:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law which can keep the real system within a small bound of a nominal trajectory planned with the learned dynamics .