A vehicle includes a transmission, an engine, a clutch, and a controller. The transmission has an input. The engine is configured to generate and deliver torque to the input. The clutch is configured to connect and disconnect the engine from the input, and to crank the engine during an engine start. The controller is programmed to, in response to a command to adjust a torque of the clutch during an engine start and a presence of first condition of the clutch, drive a clutch actuator pressure to a first desired value based on a first transfer function. The controller is further programmed to, in response to a command to adjust the torque of the clutch during the engine start and a presence of a second condition of the clutch, drive the clutch actuator pressure to a second desired value based on a second transfer function.