This paper develops a method for estimating the state of deterioration of a friction drive system and presents its use for predicting and controlling the Remaining Useful Life (RUL) of such a system. The friction drive system is assumed to be affected by endogenous uncertainties and exogenous disturbances. The proposed method is intended for on-line estimation of the contact surface deterioration and it is based on a parameter-varying model that includes both the motion dynamics and the deterioration dynamics of the device. Since, in the presented setting, the control actions on the mechanical system play a role on the non-linear deterioration dynamics, an Extended Kalman Filter is developed for simultaneously estimating both the state of deterioration and its associated estimation error bounds. A numerical example is presented to illustrate the interest of such estimations for RUL prognosis and RUL control. The presented example considers the availability of angular speed measurements and the possibility of re-planning motor torques and/or re-planning desired angular speeds in order to control RUL based on RUL prognosis.