The invention relates to motor vehicles having a power-assisted steering rack. The maximum current strength flowing through the electric power-assistance motor is controlled so as to adapt the assistance torque to the approach of the end-of-travel positions of the rack. Said control is carried out or activated on the basis of parameters including the acceleration value of the rotation of the steering wheel, and by controlling the assistance torque so as to target a deceleration value or profile of the rotation of the steering wheel, thereby making it possible to reduce the shocks and noise when the steering system reaches the steering lock stop.