One proposed power output apparatus is mounted on a vehicle that is equipped with an engine and a hydraulically-driven clutch to connect and disconnect the power transmission from the engine to drive wheels (see, for example, Japanese Patent Laid-Open Gazette No. 2003-74683). When the engine is separated from the power transmission to the drive wheels by means of the clutch and stops, this proposed power output apparatus performs a low pressure control to regulate the hydraulic pressure to a low hydraulic pressure level immediately before generation of an engagement force in the clutch. Upon satisfaction of engine restart conditions other than a vehicle start request, the power output apparatus performs feedback control to regulate the hydraulic pressure level immediately before generation of the engagement force in the clutch, based on the rotation speeds on both ends of the clutch. In response to a vehicle start request, the power output apparatus learns the regulated hydraulic pressure by feedback control as a hydraulic pressure for a next cycle of the low pressure control.