Before revision:  Our method imposes a check for the existence of the feedback law as constraints in a sampling-based planner, which returns a feedback policy ensuring that under the true dynamics, the goal is reachable, the path is safe in execution, and the closed-loop system is invariant in a small set about the goal.
After revision:  Our method imposes a check for the existence of the feedback law as constraints in a sampling-based planner, which returns a feedback policy around a nominal plan ensuring that, if the Lipschitz constant estimate is valid, the true system is safe during plan execution, reaches the goal, and is ultimately invariant in a small set about the goal.