According to first quantity of state control, a rich spike is executed while actuating a WGV so as to decrease turbocharging pressure, and after completion of the rich spike, the WGV is actuated to raise the turbocharging pressure again, the combustion air-fuel ratio is adjusted to the theoretical air-fuel ratio while suppressing an air amount by a throttle so as not to vary shaft torque until the turbocharging pressure is restored, and upon the turbocharging pressure being restored the air amount is increased by the throttle and the combustion air-fuel ratio is returned to a lean air-fuel ratio. According to second quantity of state control, a rich spike is executed while actuating the WGV so as to maintain the turbocharging pressure, and after completion of the rich spike, the air amount is increased by the throttle and the combustion air-fuel ratio is returned to a lean air-fuel ratio.