Various systems and methods are disclosed for controlling an internal combustion engine system having an internal combustion engine, and a fuel injector which directly injects fuel into a combustion chamber of the internal combustion engine. One example method comprises, when a desired torque for the internal combustion engine system is in a first range, injecting a first stage fuel into the combustion chamber so that it ends during a middle stage of a compression stroke at the latest in a cylinder cycle; determining combustion of the first stage fuel initiated by its compression self-ignition; and injecting a second stage fuel into the combustion chamber in a period when the determined combustion of the first stage fuel continues at a timing determined so as to cause combustion of the second stage fuel with its compression self-ignition.