Active control of thermoacoustic instabilities has been an important topic of research for many years. In particular, adaptive-control approaches are continually investigated because of their potential ability to adjust to changing and unknown operating conditions. Most adaptive controllers are model based and require accurate knowledge of the plant to which they are applied; this is currently an extremely challenging solution for the limit-cycling combustion plant. A more versatile controller approach, based on a gradient descent algorithm, is presented here. The time-averaged gradient controller can automatically adapt to changing plants and can assume a variety of different controller architectures and actuator styles, without the need for any explicit knowledge of the plant dynamics. We present the controller in a variety of forms and provide simulation and experimental results illustrating its effectiveness in stabilizing an unstable Rijke tube combustor and a 50-kW kerosene-fueled lean direct-injection combustor.