Various systems and methods are disclosed for controlling an internal combustion engine system having an internal combustion engine, a fuel injector which directly injects fuel into a combustion chamber of the internal combustion engine, and a supercharger which supercharges air into the combustion chamber. One example method comprises, injecting fuel into the combustion chamber multiple times so that a first part of the fuel is self ignited and a last part of the fuel being injected during the compression stroke or later in a cylinder cycle when a desired torque of said internal combustion engine system is in a first range; and increasing a pressure of air which the supercharger charges into the combustion chamber as amount of fuel injected into the combustion chamber during a cylinder cycle increases when the desired torque is in the first range.