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.
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 , and ensure the estimate is valid with a given probability . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists.