A numerical positioning control system renders possible clocked-synchronous acceleration, and deceleration operations for motorized driving systems (A). A specified target point (PO), which for example can be the end point of a path section, can be reached with a predetermined final velocity (V.sub.END) exactly at a calibration time (T) of the numerical control. At least two acceleration values (a.sub.1,a) are defined for the acceleration, and braking operation, whereby the time which is required for the entire acceleration operation is exactly an integral multiple of the calibration time (T) of the numerical control. To avoid sudden changes in acceleration, a rate-of-change limiter is implemented according to the principle of discrete convolution.