A vehicle includes an engine, an electric machine, a disconnect clutch, and a controller. The engine and the electric machine are each configured to generate power. The disconnect clutch is disposed between the engine and the electric machine. The controller is programmed to, in response to a command to start the engine, close the disconnect clutch to transfer power from the electric machine to the engine. The controller is further programmed to control the torque of the disconnect clutch via increasing a pressure applied to the disconnect clutch based on a first-order model of the pressure applied to the disconnect clutch. The controller is further programmed to adjust the model based on a difference between an expected pressure to the disconnect clutch and a measured pressure of the disconnect clutch during a time period prior to transferring torque through the disconnect clutch.