The present invention relates to methods for robust controlled auto-ignition and spark ignited combustion controls in gasoline direct-injection engines, including transients, using either exhaust re-breathing or a combination of exhaust re-compression and re-breathing valve strategy. These methods are capable of enabling engine operation with either lean of stoichiometric or stoichiometric air/fuel ratio for oxides of nitrogen (NOx) control, with varying exhaust gas recirculation (EGR) rates and throttle valve positions for knock control, and with a combination of homogeneous charge compression ignition (HCCI) and spark ignition (SI) combustion modes to optimize fuel economy over a wide range of engine operating conditions.