Bringing a cart with oscillators to a given state in the presence of perturbations

A control problem for a cart that moves along a horizontal straight line under a bounded steering force in the presence of unknown small perturbation is considered. Two linear oscillators are attached to the cart. We observe only the coordinate and velocity of the cart, while the phase states of the oscillators are unknown. A control law which in a finite time stops the cart at a given terminal state and then holds it there is proposed.