Time-optimal control of a servomechanism requires a nonlinear control law based on a switching function. The switching function depends on the characteristics of the actuator and on the load. In practical servomechanisms the friction load may be unknown and may slowly vary. In such cases the optimal switching function is unknown prior to the start of each move. A controller is developed which estimates the optimal switching function during each move, thus enabling near time-optimal control to be achieved. The controller allows for certain nonlinearities in the actuator and in the friction/velocity function, and avoids the problems of chattering and limit cycling normally associated with time-optimal control. Experimental results are presented.