In a supersonic state, the aero-engine operates under harsh circumstances of elevated temperature, high pressure, and rapid rotor speed. This work provides an innovative high-stability control technique for engines with fixed-geometry inlets, addressing stability control issues at the aero-propulsion system level. The discussion begins with the importance of an integrated model for the intake and the aero-engine, introducing two stability indices (surge margin and buzz margin) to characterize inlet stability. A novel predictive model for engine air mass flow is developed to address the indeterminate issue of engine air mass flow. The integration of input parameters in the predictive model is refined using the least squares support vector regression (LSSVR) algorithm, and historical input data is used to enhance predictive performance, as validated by numerical simulation results. A data-driven adaptive augmented linear quadratic regulator (d-ALQR) control technique is suggested to adaptively modify the control parameters of the augmented linear quadratic regulator. A highly stable control strategy is finally proposed, integrating the predictive model with the d-ALQR controller. The simulation results conducted during maneuvering flight operations demonstrate that the developed high-stability controller can maintain the inlet in an efficient and safe condition, ensuring optimal compatibility between the engine and the inlet.