1. An auto-ignition type internal combustion engine, comprising: at least one cylinder; a fuel injection system performing injection of gasoline fuel for one cycle to create stratified charge in the cylinder; a sensor generating a sensor signal indicative of combustion event timing of the created stratified charge in the cylinder; and an engine controller determining an actual value of a characteristic parameter representing combustion event timing in the cylinder from the sensor signal, and modifying at least one operating variables governing injection for the subsequent cycle in such a direction as to decrease a deviation between the actual value of the characteristic parameter and a target value thereof toward zero.