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Advanced electrified aircraft propulsion (EAP) concepts with integrated power, propulsion, and thermal systems require the development of equally sophisticated controllers to fly safe and efficient missions. Hybrid electric aircraft utilize electric machines mechanically coupled to the engine shafts to extract and insert power for a variety of purposes. Additionally, electric machines may drive propulsive fans pulling from a combination of on-board energy storage devices and engine extracted power. NASA’s investment in hybrid electric aircraft hardware-in-the-loop testing enables controls research on representative engine models using a novel emulation and scaling methodology. High-voltage, high-power electrical powertrain presents several technical risks at altitude. High-power requires high efficiency to minimize losses. Superconducting electric machines and power distribution research at NASA has identified key challenges with potential controls solutions. These risks necessitate the development of controllers robust to model uncertainty, disturbances, and fault conditions. System health management and fault detection schemes play an important role in a multi-layer controls approach that utilizes a supervisor which oversees inner loops for the highly coupled power, propulsion, and thermal systems. Such a supervisory controller enables coordinates energy transfer between engines, energy storage devices, electric machines, propulsors, and heat exchangers. Existing methods have shown an improvement in engine operability using the hybrid electric powertrain.