Combustion instabilities in lean premixed combustion are one of the most prevalent challenges that arise in gas turbines. If not addressed, these instabilities can result in serious performance degradation and mechanical failure. Active control techniques have been used to reduce these instabilities. However, open-loop controllers have a limited operational range, and closed-loop controllers usually require high-bandwidth actuators. The present work considers adaptive control, where the feedback control law operates with a low bandwidth relative to the open-loop dynamics of the combustor, and adapts to a wide range of operating points. An adaptive digital controller is applied to a swirl-stabilized gas turbine model combustor called the Dual Independent Swirl Combustor (DISCo) with the primary objective of reducing the amplitude of the combustion instabilities. The results of several tests performed on the model combustor are shown, which demonstrate the effectiveness of the adaptive controller.