A direct injection controlled auto-ignition engine is operated at steady state, within a homogeneous charge compression-ignition (HCCI) load range and with fuel-air-diluent mixtures at predetermined conditions, for each speed and load, of engine control inputs, including at least injection timing (FI), spark timing (SI), throttle position, exhaust gas recirculation (EGR) valve setting and exhaust recompression obtained by negative valve overlap (NVO). During engine speed transients, the control inputs are synchronized to changes in the current engine speed, and also with any concurrent changes in the engine fueling rate. Inputs that are inactive during all or part of a speed change have a zero change rate while inactive. The method maintains robust auto-ignition combustion during speed transients with constant or variable fueling rates and with or without load changes.