An operating system for a vehicle having an engine that provides an input shaft into a split-power transmission to actuate an output shaft that drives an axle and wheels of the vehicle. The split-power transmission uses a power summing device in order to provide a plurality of modes that are associated with a plurality of clutching and variable power units. By using the power summing device in association with the plurality of clutches and variable power units, a controller that is electrically connected to each is able to actuate the clutches and variable power units in order to provide an automatic transmission that shifts at synchronous speeds.