Control of the combustion process under hypersonic conditions remains a challenging problem. In this paper, we investigate the application of a data-driven, learning-based control technique to regulate a combustion process evolving inside a solid fuel ramjet to regulate the generated thrust under unknown operating conditions. A computational model to simulate the combustion dynamics is developed by combining compressible flow theory with equilibrium chemistry. The computational model is simulated to ascertain the combustion dynamics' stability and establish the engine's operational envelope. Based on retrospective cost optimization, an online learning controller is then integrated with the computational model to regulate the generated thrust. Numerical simulation results are presented to demonstrate the robustness of the adaptive control system.