To prevent continuation of the state where the output shaft torque is largely fluctuated.

The control device estimates the self-ignition timing at which a mixed gas is self-ignited. The control device corrects the exhaust valve closing timing and the suction valve opening timing so that the negative overlap period is prolonged as the estimated self-ignition timing Sest is advanced further. Thus, a combustion gas of the volume to be increased as the self-ignition timing is advanced further is fed to the next combustion cycle. As a result, even when the temperature of a remaining combustion gas is dropped by the advancement of the self-ignition timing, excessive drop of the compression start temperature of the next combustion cycle is prevented, and the range of the fluctuation of the self-ignition timing associated with the elapse of the combustion cycle is reduced.

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