A method controls a movement of a train to a stop at a stopping position between a first position and a second position. The method determines constraints of a velocity of the train with respect to a position of the train forming a feasible area for a state of the train during the movement, such that an upper curve bounding the feasible area has a zero velocity only at the second position, and a lower curve bounding the feasible region has a zero velocity only at the first position. Next, the method controls the movement of the train subject to the constraints.