Changing the combustion process of a gas turbine from a constant-pressure to a pressure-increasing approximate constant-volume combustion (aCVC) is one of the most promising ways to increase the efficiency of turbines in the future. In this paper, a newly proposed method to achieve such an aCVC is considered. The so-called shockless explosion combustion (SEC) uses auto-ignition and a fuel stratification to achieve a spatially homogeneous ignition. The homogeneity of the ignition can be adjusted by the mixing of fuel and air. A proper filling profile, however, also depends on changing parameters, such as temperature, that cannot be measured in detail due to the harsh conditions inside the combustion tube. Therefore, a closed-loop control is required to obtain an adequate injection profile and to reject such unknown disturbances. For this, an optimization problem is set up and a novel formulation of a discrete extremum seeking controller is presented. By approximating the cost function with a parabola, the first derivative and a Hessian matrix are estimated, allowing the controller to use Newton steps to converge to the optimal control trajectory. The controller is applied to an atmospheric test rig, where the auto-ignition process can be investigated for single ignitions. In the set-up, dimethyl ether is injected into a preheated air stream using a controlled proportional valve. Optical measurements are used to evaluate the auto-ignition process and to show that using the extremum seeking control approach, the homogeneity of the ignition process can be increased significantly.