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Bounded control of elastic linear mechanical system with unknown parameters

A controlled mechanical system represented by a line of rigid bodies connected with each other by telescopic hinges or springs is considered. We assume that the masses of the bodies and the stiffness of the springs are unknown, and the control forces are bounded. A control law based on the linear feedback with time-varying gains is developed which makes the spring oscillations sufficiently small and brings the hinges to a prescribed terminal position in a finite time.