A Review of Hybrid-Electric Propulsion in Aviation: Modeling Methods, Energy Management Strategies, and Future Prospects

Abstract

Aviation is under increasing pressure to reduce carbon emissions in conventional transports and support the growth of low-altitude operations such as long-endurance eVTOLs. Hybrid-electric propulsion addresses these challenges by integrating the high specific energy of fuels or hydrogen with the controllability and efficiency of electrified powertrains. At present, the field of hybrid-electric aircraft is developing rapidly. To systematically study hybrid-electric propulsion control in aviation, this review focuses on practical aspects of system development, including propulsion architectures, system- and component-level modeling approaches, and energy management strategies. Key technologies in the future are examined, with emphasis on aircraft power-demand prediction, multi-timescale control, and thermal integrated energy management. This review aims to serve as a reference for configuration design, modeling and control simulation, as well as energy management strategy design of hybrid-electric propulsion systems. Building on this reference role, the review presents a coherent guidance scheme from architectures through modeling to energy-management control, with a practical roadmap toward flight-ready deployment.

1. Introduction

Aviation is being reshaped by two converging pressures: the drive to decarbonize conventional transport aircraft and the need to make low-altitude operations economically viable at scale. The former is governed by increasingly stringent limits on fuel burn, noise, and emissions; the latter is constrained by the endurance and power-density limits of battery-electric eVTOLs. Taken together, these driving factors motivate the development of hybrid electric propulsion, which combines the high specific energy of liquid fuels with the controllability of electrified powertrains. Equally important are the associated methods of modeling, control, and energy management that are required to transform the architectural potential of such systems into demonstrable mission performance. The background that follows develops these twin motivations in turn.

As global air transport continues to expand, concerns over fuel burn, noise, and pollutant emissions have intensified. In response, the United States and the European Union have articulated ambitious targets for the next generation of commercial aircraft. The European Union’s Clean Aviation initiative (launched in 2021) prioritizes hybrid-electric regional aircraft, ultra-efficient short/medium-range aircraft, and hydrogen-powered concepts. Its roadmap envisions initial deployment as early as 2035, with goals of roughly a 50% reduction in fuel consumption relative to state-of-the-art 2020 aircraft and up to a 90% reduction in emissions contingent on extensive use of alternative fuels [1]. The UK Aerospace Technology Institute’s FlyZero project (2022) likewise targets net-zero aviation by 2050 and identifies more than ten enabling technologies, notably cryogenic hydrogen storage and hybrid-electric propulsion architectures [2]. Complementing these efforts, Aeronautics Research Mission Directorate of National Aeronautics and Space Administration (NASA, Washington, DC, USA) released its 2023 strategic implementation plan to advance sustainable aviation via reductions in emissions, fuel consumption, and noise [3]. To meet these objectives, Electric Aircraft Propulsion (EAP) has emerged as a leading pathway for commercial air transport [4]. Fully electric architectures are already viable for small, short-range aircraft; however, for larger transports, the specific energy of current electrochemical storage remains insufficient to surpass kerosene-fueled gas-turbine performance in the foreseeable future [5]. Consequently, hybrid-electric propulsion has gained momentum as a near- to mid-term solution that can bridge this gap. Compared with conventional architectures, integrating electric machines and power electronics with gas-turbine cores introduces tight static and dynamic couplings across the propulsion system by offering new degrees of freedom to improve turbomachinery operability and efficiency while simultaneously posing fresh challenges for system modeling and control. NASA has been heavily involved in research on electrified propulsion systems in recent years and has summarized the guidelines for modifying the performance of engine components and the design concept of the energy management control schedule: turbine electrified energy management (TEEM) [6,7,8,9,10]. The TEEM control strategy concept has already been preliminarily applied in the pre-research of several large-thrust hybrid aircraft concepts, including the Boeing (Arlington, VA, USA) SUGAR Volt and NASA STARC-ABL configurations.

In the field of low-altitude aircraft, electric vertical takeoff and landing (eVTOL) aircraft—owing to their high operational efficiency and runway-independent VTOL capability—are widely regarded as promising platforms for developing the low-altitude economy [11,12]. However, the endurance of current battery-electric eVTOLs is still strongly constrained by the limited specific energy of batteries and the high power demand during VTOL phases, which restricts mission duration in many use cases [13,14,15,16]. Hybrid-electric propulsion, which combines the high specific energy of fuel-based prime movers with the flexibility of electrified power transmission, provides a credible pathway to mitigating these range and endurance limitations [17,18]. Realizing the full endurance potential of hybrid eVTOLs and maximizing mission range under “full fuel and full charge” conditions requires intelligent energy-management capable of achieving near-optimal energy economy under multiple constraints and dynamically varying flight environments. While sophisticated energy-management strategies are mature in hybrid-electric road vehicles, hybrid aircraft remain at an early stage and often rely on rule-based schemes [19,20]. In real-time operations, AI-enabled energy management, for example, safe reinforcement-learning approaches trained offline and executed on modest onboard hardware has shown promise in improving decision quality and adaptability under dynamic conditions [21,22].

Compared with road-vehicle hybrids, the aviation problem that EMS must solve is defined by different fundamentals: power demand is forecast by mission segment (VTOL/transition, climb, cruise, descent, go-around/loiter) with explicit reserve planning, not by road cycles; operations occur in altitude- and weather-dependent environments (density, temperature, turbulence, icing) that reshape available thrust and electrical/thermal margins; the plant dynamics and prime movers differ (turboshaft/turboprop cores with spool and surge behavior driving propellers, rather than ground piston drivetrains), and mass sensitivity is far greater, making every kilogram a range and climb penalty. These factors require models that expose the right states and envelopes. Where applicable, assurance considerations favor explainable structures, but the primary differentiator from automotive is the frame of mission, environment and dynamics problem.

This review provides a systematic synthesis of hybrid-electric propulsion systems, focusing on research progress in system modeling methods and energy management strategies, and offers perspectives on future cutting-edge research directions. In terms of modeling, we delineate series, parallel, and series–parallel (mixed) architectures and compare system-level and component-level models for prime movers (gas turbines, piston engines, or fuel cells), energy storage systems (batteries), electric machines (motors/generators), and power-conditioning units. In terms of control, we categorize energy-management strategies from rule-based approaches (deterministic and fuzzy) to optimization-based methods (global and real-time) and learning-based techniques (reinforcement learning). This review aims to establish a concise and coherent foundation to support advancements in both theoretical research and engineering implementation of energy-management technologies for hybrid-electric propulsion systems. Unlike prior surveys that treat either architectures or control in isolation, this review integrates architectures, modeling methods, and energy-management strategies into a single aviation-specific framework and distills concise selection criteria to guide flight-program decisions.

The remainder of this paper is organized as a connected narrative. Section 2 establishes the technical foundation by reviewing hybrid-electric propulsion configurations and subsequently comparing system-level and component-level modeling approaches for the prime mover (engine or fuel cell), energy storage systems, electric machines, and power conditioning units. Building on this foundation, Section 3 provides a systematic examination of energy management strategies, progressing from rule-based methods to optimization-oriented approaches and ultimately to learning-driven techniques. Section 4 draws the threads together, analyzing key control and energy-management techniques in light of the preceding modeling and configuration discussion and summarizing their implications for hybrid-electric propulsion. Section 5 concludes with a synthesis of the main insights and outlines priorities for future research and flight-ready deployment.

2. Modeling: Hybrid Configuration and Method

Before examining hybrid configurations in detail, we first position them in relation to mission-specific power demands and conventional reference systems. Aircraft power and energy requirements are determined by mission phases such as takeoff and initial climb, transition or hover when applicable, cruise, and reserve operations, as well as by environmental and altitude effects including high-temperature conditions, high-altitude performance, and icing. At the same time, conventional turbomachinery imposes constraints related to spool acceleration, surge margin, turbine inlet temperature and thermal headroom, part-load efficiency, and, in the case of electrified systems, the quality of the direct current bus power. Pure-electric concepts remain range-limited by system-level specific energy, thermal management, and turnaround; pure-fuel concepts offer energy density and maturity but incur off-design penalties and cannot buffer fast electrical loads without extra hardware. These realities motivate hybridization: electrical machines provide transient/contingency assistance and enable right-sizing of the thermal prime mover, while EMS enforces explicit SOC/voltage/thermal/torque envelopes derived from tractable models.

To better highlight the advantages of hybrid configurations, we have summarized the strengths and weaknesses of aerospace hybrid propulsion configurations (series, parallel, and series-parallel) alongside traditional aerospace propulsion systems in

Table 1. Comparison of Aerospace Propulsion System Configurations.

Configuration	Required Power Sources	Energy Conversion Efficiency	Maintenance-Free Operating Time	Specific Power (kW/kg)	Size/Volume	Advantages	Disadvantages
Conventional Fuel-based	Aero-engine (turbofan/turbojet)	High (~35–40%)	Long, high reliability	Relatively high (limited by thermal efficiency)	Compact	High maturity, long range, easy refueling	High carbon emissions, fuel dependence, environmental pressure
Series Hybrid	(ICE/aero-engine + generator)/Fuel cell + battery + motor	Moderate (~25–35%), affected by multi-stage conversion	Moderate, limited by battery degradation	Moderate (restricted by battery specific energy)	Distributed configuration	Flexible motor placement, easier optimization and control	Long energy chain, efficiency losses, limited battery lifetime
Parallel Hybrid	Engine + motor (independent or combined output)	Relatively high (~30–40%), optimal source selection by mission phase	Moderate to long	Relatively high (engine and motor synergy improves power density)	Relatively compact	Flexible switching between power sources during takeoff/cruise, improved fuel economy	Higher control complexity, mechanical coupling challenges
Series-Parallel Hybrid	Engine + motor + battery + generator	Potentially higher (~35–45%), enabled by adaptive operation	Moderate to long	Relatively High (multi-source power aggregation)	Largest, most complex	Strong adaptability across mission phases, balance between endurance and emissions	Complex architecture, high cost, demanding control strategies

. With this context in place, Section 2.1 reviews the hybrid configurations that structure the subsequent modeling and control discussion.

2.1. Hybrid Configuration

The airborne electrical systems mostly adopt low-voltage DC architectures, valued for their simplicity and broad applicability. In contrast, contemporary hybrid-electric propulsion systems employ multiple energy architectures including parallel, series, and series–parallel layouts. They are powered by onboard sources such as aero engines (piston or turboshaft), hydrogen fuel cells, and lithium-ion batteries, with optional external charging for energy replenishment. In this section, under the assumption of a single DC bus, the principal hybrid configurations and their operating modes are described. We have summarized the configurations and components of existing aerospace hybrid systems, as shown in Table 2.

2.1.1. Series Hybrid System Configuration

Two representative realizations are the oil–battery hybrid and the hydrogen–battery hybrid; their topologies are analogous and illustrated in Figure 1 and Figure 2, respectively. In the configuration of Figure 1, the engine’s mechanical output drives a generator, converting all shaft power to electricity that is distributed via the DC bus to the traction motor. The motor, in turn, drives the propeller to produce thrust. The battery functions as an auxiliary energy buffer: during high-power segments (e.g., climb, acceleration) it delivers supplementary power to the motor; during lower-power flight phases (e.g., cruise, descent), the engine can be scheduled to operate near its best-efficiency region, with a portion of its generated electric power feeding the motor for propulsion and the surplus used to recharge the battery. The configuration of Figure 2 is similar to Figure 1; the fuel cell battery works as the main power source.

For power demands in the hundreds of kilowatts and above, turboshaft engines offer markedly higher power-to-weight ratios (specific power) than piston engines, making them attractive prime movers for hybrid–electric aircraft. The turbo-electric hybrid architecture has therefore emerged as a practical pathway to mitigate eVTOL range anxiety. Major aero-engine manufacturers, including General Electric (GE, Boston, MA, USA), Rolls-Royce (R-R, Derby, UK), Honeywell (Charlotte, NC, USA), and Safran (Paris, France), have developed megawatt-class turboelectric generation systems, several of which have progressed through ground and even flight demonstration, as shown in Figure 3. In 2022, GE reported a megawatt-class, kilovolt-class turbo-electric system test conducted under high-altitude conditions based on the CT7-9B turboprop and is collaborating with Boeing (United States) to support hybrid-electric flight testing [23]. Beyond GE, Rolls-Royce has developed a prototype turbo-electric system using the AE 2100 as the core engine; In November 2021, the ground test article generated >1 MW of electrical power, with a targeted 2.5 MW peak capability [24]. Honeywell, leveraging the HGT1700 auxiliary power unit as the core, achieved 900 kW continuous output and a 1.02 MW peak turbogenerator power during ground runs in May 2022 [25]. Safran, using an Ardiden turboshaft as the prototype core, completed ground testing of its Tech TP turboelectric technology demonstrator in February 2023 [26].

For the research progress on the hydrogen-electric hybrid aircraft, a representative hydrogen–battery series-hybrid powertrain is exemplified by ZeroAvia’s (Hollister, CA, USA) Dornier 228 demonstrator, in which a liquid-hydrogen (LH₂) storage system, fuel-cell stacks, and a lithium-ion battery pack supply 2–5 MW-class electric motors driving propellers; the aircraft achieved its first flight in January 2023 [27]. On 11 July 2024, Joby Aviation (Santa Cruz, CA, USA) announced a piloted hydrogen-electric hybrid air-taxi demonstration covering 523 miles, reporting water as the only by-product; the system features a Joby-designed LH₂ tank storing up to 40 kg of liquid hydrogen, thereby reducing battery mass, with hydrogen fed to an H2FLY (Stuttgart, Germany) fuel-cell system that produces electricity (with water and heat as co-products) [28]. In January 2025, China’s DF600 “Jinghong”—the country’s first ton-class hybrid tilt-rotor eVTOL to carry liquid hydrogen—completed flight verification in Baoji, Shaanxi. With a take-off weight of approximately 1.2 t and a payload capacity of 120–160 kg, the platform targets a >1000 km single-mission range. Its powertrain integrates a 37 kW air-cooled fuel-cell stack and a 30 L LH₂ storage-and-supply system employing a 30 L titanium cryogenic tank designed for 24 h zero-boil-off storage [29]. As shown in Figure 4.

2.1.2. Parallel Hybrid System Configuration

The parallel hybrid propulsion system comprises two independent prime movers including an aeroengine and an electric motor whose torques are mechanically combined to provide thrust or drive a common propeller shaft, as shown in Figure 5. A clutch enables the engine and the motor/generator to operate either jointly or independently, giving rise to four canonical modes: engine-only, electric-only, hybrid/power-assist, and charge-sustaining/charging. During high-power segments such as takeoff and climb, the engine and motor supply additive torque to the propeller; during lower-power phases such as cruise and descent, the motor can be back-driven as a generator so that the engine both propels the aircraft and recharges the battery. Parallel hybrid system offers several practical advantages for aircraft: minimal changes to the airframe and propulsor layout, lower peak ratings for electrical components, and strong capability to handle high-power/high-torque transients, which makes this architecture well suited to retrofitting legacy turbofan or turboshaft, fuel-powered fixed-wing aircraft.

Research on parallel hybrid propulsion for UAVs, eVTOLs, and small- to medium-sized transport aircraft includes several representative concepts. Boeing’s SUGAR Volt (Subsonic Ultra Green Aircraft Research) concept [30,31,32] couples a megawatt-class electric machine in parallel with the low-pressure (LP) shaft of a GE turbofan, enabling conventional kerosene operation while providing electric power assist to the LP spool when required. Georgia Institute of Technology (Georgia Tech, Atlanta, GA, USA) EVE concept [33] similarly parallels a 1.8–2.6 MW motor, with system-level studies indicating potential reductions of ≈25% in fuel burn and ≈10% in total energy consumption. United Technologies Research Center (UTRC, East Hartford, CT, USA)and Pratt & Whitney (East Hartford, CT, USA) have proposed a hybrid geared turbofan (hGTF) architecture [34] that integrates a high-speed electric machine with the LP turbine through a high-efficiency reduction gearbox, employs hybrid battery/fuel-cell energy storage, and incorporates an integrated thermal management system. Collectively, these studies underscore the feasibility and scalability of parallel hybridization for both distributed and conventional propulsion layouts.

In 2022, the EU Clean Aviation program announced a collaboration among Airbus (Toulouse, France), MTU Aero Engines (Munich, Germany), Pratt & Whitney, Collins Aerospace (Charlotte, NC, USA), and GKN Aerospace (Bristol, UK) to develop hybrid-electric and water-enhanced turbofan (WET) technologies for future transport-aircraft propulsion. The initiative aims to improve fuel efficiency and deliver short- to medium-term CO₂ reductions, with potential savings of up to 25% for short/medium-range aircraft [1]. In parallel, Airbus has proposed hybrid-propulsion concept studies for platforms including the ATR 72 and the A320/A330 families [35].

2.1.3. Series-Parallel Hybrid System Configuration

The series-parallel hybrid system configuration (Figure 6) combines the advantages of series and parallel layouts, balancing electrification depth with technical feasibility and allowing mode switching across flight phases: a parallel (power-assist) mode during takeoff, with the turboshaft/turbofan and motor delivering peak combined power; a series (turbogenerator) mode in cruise, where the engine drives a generator to supply the traction motor and any surplus recharges the battery; and a regenerative mode in descent to recover braking energy. This dynamic reconfiguration supports high efficiency over the full mission profile and is often viewed as a transitional solution for medium- to long-range aircraft.

A representative concept is NASA’s single-aisle turboelectric aircraft with an aft boundary-layer-ingesting (BLI) fan (STARC-ABL). An electrically driven, fuselage-embedded tail fan is powered by generators coupled to the two under-wing turbofan engines. By ingesting the slower fuselage boundary layer and re-energizing the wake, the aft fan reduces overall drag. In this arrangement, the under-wing engines provide roughly 80% of the takeoff thrust and about 55% of the cruise thrust, with the embedded fan supplying the remainder; relative to a conventional configuration, the STARC-ABL architecture is projected to reduce fuel burn by 7–12% [36].

Although this configuration can exploit the advantages of both series and parallel schemes, it also tends to increase propulsion-system complexity and mass. These penalties place significant demands on aircraft-level design, including integration of multiple power paths, packaging and weight distribution, and the coordination of controls and thermal management, thereby posing substantial challenges for overall configuration sizing and optimization.

Based on published literature and reports, the conceptual design and tested hybrid systems are summarized as follows:

Table 2. Configuration summary.

Program/ Model	Test/Expected Timeframe	Hybrid Configuration	Components	Component Performance	Ref.
DA36 E-Star2	2013	Series hybrid	Wankel engine Generator	70 kW	[37]
X-57 Maxwell	2014	Series hybrid	Motor Battery	2 × 60 kW 12 × 9 kW	[38]
SONG	2014	Parallel hybrid	Engine Motor/Generator	7.5 kW 12 kW	[39]
GL-10	2015	Series hybrid	Generator Motor	6 kW, 20 kW, 45 kW	[40]
LightningStrike	2016	Series hybrid	AE1107C turboshaft Generator Ducted fans	_	[41]
LUH Germany	2018	Parallel hybrid	Engine Motor	4 MW	[35]
ZA10	2018	Series hybrid	Turboshaft Ducted fan Battery	500 kW 500 kW 500 kW	[42]
Surefly	2018	Series hybrid	Piston engine Generator Motor	150 kW - -	[43]
HEPS	2019	Series hybrid	Turbogenerator Battery	600 kW	[26]
HEMEP	2019	Series hybrid	AE300 diesel engine Motor Battery	110 kW 75 kW 12 kWh	[26]
PGS1	2021	Series hybrid	High–power-density PM motor Li-ion battery	2.5 MW 300 Wh/kg	[39]
Cambridge	~2030	Parallel hybrid	Battery	750 Wh/kg	[44]
EVE	~2030	Parallel hybrid	Motor Battery	1.8–2.6 MW 750 Wh/kg	[33]
UTRC	~2030	Parallel hybrid	Motor Battery	2.1 MW	[5]
UTRC	~2030	Auxiliary power unit (fuel cell, cryogenic fuel)	Generator	3–10 kW/kg	[5]
Boeing SUGAR	~2030	Parallel hybrid	Motor (1.3–5.3 MW) Battery	3–5 kW/kg 750 Wh/kg	[31]
E-Thrust	~2040	Series hybrid	Turbofan Generator Ducted fans	9 MW	[45]
Boeing SUGAR	~2040	Parallel hybrid (fuel cell, superconducting, cryogenic fuel, BLI)	Motor Battery	8–10 kW/kg 1000 Wh/kg	[31]

Table 2. Configuration summary.

Program/ Model	Test/Expected Timeframe	Hybrid Configuration	Components	Component Performance	Ref.
DA36 E-Star2	2013	Series hybrid	Wankel engine Generator	70 kW	[37]
X-57 Maxwell	2014	Series hybrid	Motor Battery	2 × 60 kW 12 × 9 kW	[38]
SONG	2014	Parallel hybrid	Engine Motor/Generator	7.5 kW 12 kW	[39]
GL-10	2015	Series hybrid	Generator Motor	6 kW, 20 kW, 45 kW	[40]
LightningStrike	2016	Series hybrid	AE1107C turboshaft Generator Ducted fans	_	[41]
LUH Germany	2018	Parallel hybrid	Engine Motor	4 MW	[35]
ZA10	2018	Series hybrid	Turboshaft Ducted fan Battery	500 kW 500 kW 500 kW	[42]
Surefly	2018	Series hybrid	Piston engine Generator Motor	150 kW - -	[43]
HEPS	2019	Series hybrid	Turbogenerator Battery	600 kW	[26]
HEMEP	2019	Series hybrid	AE300 diesel engine Motor Battery	110 kW 75 kW 12 kWh	[26]
PGS1	2021	Series hybrid	High–power-density PM motor Li-ion battery	2.5 MW 300 Wh/kg	[39]
Cambridge	~2030	Parallel hybrid	Battery	750 Wh/kg	[44]
EVE	~2030	Parallel hybrid	Motor Battery	1.8–2.6 MW 750 Wh/kg	[33]
UTRC	~2030	Parallel hybrid	Motor Battery	2.1 MW	[5]
UTRC	~2030	Auxiliary power unit (fuel cell, cryogenic fuel)	Generator	3–10 kW/kg	[5]
Boeing SUGAR	~2030	Parallel hybrid	Motor (1.3–5.3 MW) Battery	3–5 kW/kg 750 Wh/kg	[31]
E-Thrust	~2040	Series hybrid	Turbofan Generator Ducted fans	9 MW	[45]
Boeing SUGAR	~2040	Parallel hybrid (fuel cell, superconducting, cryogenic fuel, BLI)	Motor Battery	8–10 kW/kg 1000 Wh/kg	[31]

2.2. Modeling Method

To assess the performance of a candidate hybrid-electric propulsion architecture, we use a model that couples all relevant subsystems and lets them operate consistently within the same simulation. This section introduces two scales of work: system-level models and component-level models.

2.2.1. System-Level Modeling

At the system level, models are commonly grouped by fidelity into two families: power-flow models and physics-based models.

(1)

Power-flow models

Power-flow models describe the steady distribution and transfer of electrical power. The system is represented as a network of buses and lines, and major components (motors, generators, batteries, converters) are modeled as modular blocks with static maps and algebraic power-balance equations. The approach is modular, fast to run, and easy to combine with mechanical and aerodynamic subsystems, so it suits architecture trade studies and controller development. Although designed for steady-state analysis, quasi-steady extensions can capture limited dynamics. NASA’s EMTAT library illustrates this methodology [46]: a modular electric-distribution model built with power/load-flow techniques is co-simulated with gas-turbine mechanics. In MATLAB/Simulink, plug-and-play blocks, coupled electromechanical dynamics, and short simulation times are typical; comparisons with NASA’s electric-aircraft test platform show adequate accuracy for steady and mildly transient regimes.

(2)

Physics-based models

Physics-based models use conservation laws and established relations from aerodynamics, thermodynamics, electromechanics, and structural mechanics to describe subsystem behavior. Examples include aero-engine thermodynamic cycle models, dynamic electromechanical models, detailed loss models for machines, and fuel or hydrogen consumption maps. Common multi-physics platforms are MATLAB/Simulink (https://www.mathworks.com, accessed on 25 August 2025), Dymola (Based on Modelica) (https://www.3ds.com/products-services/catia/products/dymola/, accessed on 25 August 2025), and AMESim (https://www.plm.automation.siemens.com/global/en/products/simcenter/simcenter-amesim.html, accessed on 25 August 2025). Simulink offers extensive electrical libraries that integrate with control blocks for controller-in-the-loop studies. Modelica is an object-oriented, equation-based, multi-domain language that supports tight coupling across electrical, mechanical, thermal, and control domains for complex co-simulation [47]. AMESim is a system-engineering multi-physics environment used widely for aero-engine and hybrid-propulsion studies; its electrical, transmission, gas-turbine, and thermo-fluid libraries support physics-level modeling [48].

A comparison of the two system-level modeling approaches for hybrid-electric propulsion is provided in

Table 3. Comparison of the two system-level modeling approaches.

Model Type	Modeling Focus	Digital Platform	Advantages	Limitations	Primary Uses
Power-flow model	System power connectivity and allocation; bus voltages and load relationships	Simulink (NASA’s EMTAT library)	Fast simulation; modular structure; easy integration with non-electrical subsystems	Limited dynamic fidelity (mainly steady/quasi-steady analysis)	Controller prototyping; overall performance assessment
Physics-based model	Internal device mechanisms; coupled losses; true dynamic responses	Simulink (Simscape library), Dymola (Modelica), AMESim	High theoretical accuracy; suitable for detailed analyses	High complexity and computational cost; strong parameter dependence	Optimal/control co-design; real-time energy management development; high-fidelity performance simulation

.

2.2.2. Component-Level Modeling

Hybrid-electric aircraft include many subsystems and strong couplings across mechanical, electrical, and thermal domains. Each component should be modeled with a method that fits the study goal and the required fidelity.

(1) Aero-engine modeling: Two main approaches are used: physics-based models and identification-based models. Physics-based models build mathematical descriptions of each component from conservation laws of mass, energy, and momentum and from established component relations. They offer clear physical interpretation and suit large, complex engines, but accuracy depends on detailed parameters and on simplifications that may not capture all real effects. Identification-based models fit input–output dynamics from experiments or high-fidelity simulations. They handle nonlinear, time-varying behavior and allow rapid model development for a defined operating envelope, yet their performance depends on data quality and on the robustness of the identification method.

Aero-engine modeling tools have matured over decades. In the 1990s, NASA Glenn and its partners developed the Numerical Propulsion System Simulation (NPSS) for detailed whole-engine simulations [49,50]. In 2014, NASA released the Thermodynamic Modeling and Analysis Toolbox (T-MATS) for MATLAB/Simulink, which packages turbomachinery components as reusable Simulink blocks and provides a framework for complex thermodynamic system studies [51]. Comparable European platforms include Gas Turbine Simulation Program (GSP, Rotterdam, The Netherlands; https://www.gsp.eu.com, accessed on 25 August 2025). [52], GasTurb Turbine Simulation Software (GasTurb, Aachen, Germany; https://www.gasturb.de, accessed on 25 August 2025) [53], and Process Oriented Simulation Software (PROOSIS, Madrid, Spain; https://ecosimpro.com/products/proosis/, accessed on 25 August 2025) [54]. GSP is a component-based environment for gas-turbine performance analysis with steady and transient capability. GasTurb supports cycle design and performance evaluation for turbojet, turbofan, turboprop, turboshaft, ramjet, and industrial gas turbines, and supplies the needed component parameters. PROOSIS, built on EcosimPro, offers an interactive setting to build mathematical models of physical systems and to solve the associated numerical problems for gas-turbine applications.

(2) Fuel-cell modeling: Fuel cells are another common primary power source in hybrid-electric aircraft. A typical system includes the stack and the air and hydrogen supply subsystems, whose interactions sustain overall operation. In hydrogen–electric hybrids, models often focus on the stack’s electrical performance, with less attention to auxiliary-subsystem dynamics. Stack models are usually grouped into mechanistic/physics-based models [55], empirical models [56,57], and data-driven models [58,59]. Mechanistic models solve coupled fluid-flow, heat-transfer, and electrochemical-reaction equations to track mass and energy transport with high fidelity. They are physically transparent but parameter-intensive and computationally heavy, which limits day-to-day engineering use. Empirical models start from physical insight but replace detailed physics with calibrated relationships, so they are lower order, need fewer parameters, and run faster, which suits control design. Data-driven models fit input–output relations from extensive experiments; they can be built quickly for a target operating range, but they depend on data quality and extrapolate poorly.

In practice, polarization curves, efficiency maps, and other fuel-cell performance data are often implemented as lookup tables [60,61]. High-fidelity models predict behavior more accurately but at higher computational cost. Control design therefore seeks a balance between accuracy and complexity. For energy-management in hydrogen–electric hybrid aircraft, map-based implementations constructed from calibration data and accessed via lookup tables are an effective and pragmatic choice.

To interface these models with EMS, aging and thermal coupling should be represented explicitly, even for map-based implementations, using lightweight surrogates that preserve deterministic timing. A practical construction is to maintain a stack-health state (for example, a voltage-decay or loss-of-active-area proxy) updated from load and temperature histories, combined with temperature-dependent polarization/efficiency maps and air/H₂ supply limits that reflect altitude and ambient extremes. These health and thermal states enter EMS as hard windows (stack-temperature and humidity/flow bounds) and cost terms (aging penalties), enabling power-split decisions that trade short-term efficiency against long-term durability without invoking full multiphysics models.

(3) Energy-storage battery modeling: Lithium-ion batteries are typically used. Modeling falls into three groups: physics-based electrochemical models, equivalent-circuit models, and data-driven models, as shown in Figure 7.

Typical electrochemical models include the single-particle model (SPM) [62,63] and the pseudo-two-dimensional (P2D) model [64,65,66]. The SPM represents each electrode with one representative particle to capture solid-phase diffusion; fidelity is limited. The P2D model treats the electrodes as porous media filled with electrolyte and uses coupled PDEs for concentrations and potentials in both phases. It can reflect main and side reactions, but the computational cost is high and limits routine use.

Equivalent-circuit models (ECMs) reproduce battery behavior with electrical elements and are commonly divided into integer-order ECMs [60,67] and fractional-order ECMs [68,69]. Integer-order models use few parameters and run quickly; the simplest is the R_int model, which uses an ideal voltage source in series with a resistor [60]. These models often work well in hybrid hydrogen–electric EMS studies, but they do not capture constant-phase-element behavior seen in impedance spectra. Fractional-order ECMs improve fidelity at the price of more parameters and heavier computation and are preferred when accurate state-of-charge estimation is required. Overall, ECMs are simple, reliable, and relatively easy to identify, which suits applications with tight real-time constraints.

Data-driven models [70,71,72] learn input–output relations from measurement data without resolving internal reactions. They can represent strong nonlinearities, but performance depends on data quality and coverage, and physical interpretability is limited.

To interface battery models with EMS, aging and thermal effects should be represented explicitly, even when using ECM or FO-ECM structures, in a lightweight form that preserves deterministic timing. A practical construction is to maintain an explicit but reduced set of SOH states, such as capacity fade and resistance growth driven by temperature and C-rate histories and compatible with ECM/FO-ECM identification. Thermal coupling can be captured through a lumped core–shell temperature or an external temperature input linked to operating envelopes. In EMS, these variables act as constraints—minimum SOC/SOH margins and temperature limits—and as penalties through degradation-cost terms, enabling multi-objective scheduling that balances instantaneous economy with lifetime targets under onboard real-time constraints.

(4) Generator and Motor modeling: In a hybrid-electric powertrain, the generator is usually coupled to the aero-engine as a range extender and provides the primary electrical supply, while the traction motor drives the propulsor. Physics-based generator models draw on electromagnetics, rotor dynamics, and heat transfer to capture coupled electrical–mechanical–thermal behavior across the operating envelope. They support high-fidelity design studies but are computationally demanding, especially for multiphase machines and nonlinear regimes, and they require extensive parameter calibration and test data [73,74,75]. Reduced models simplify the loss picture or retain only dominant power-flow paths; they run quickly and suit early architecture trades, at the cost of accuracy [76]. Identification-based models fit input–output dynamics from experiments or high-fidelity simulations, which is useful when detailed physics are unavailable or the system is too complex for full mechanistic treatment; their predictive quality depends on data coverage and the robustness of the identification method [77]. Hybrid, or gray-box, formulations embed governing structure and identify uncertain parameters to balance interpretability with practical accuracy and are increasingly used for complex machine models and control co-design.

For the propulsion motor, models are often built for permanent-magnet synchronous machines (PMSM/PMSG) to represent voltage production, torque generation, and realistic dynamics in motoring and generating modes. Modular coupling with the aeroengine, rectifier, and DC link helps capture key subsystem interactions in hybrid architectures [78,79]. Equivalent-circuit and dq-axis models are standard for control design and system studies; finite-element or multiphysics surrogates are added when detailed loss or thermal behavior is needed. Common control choices include proportional–integral field-oriented control for PMSMs and scalar V/f control for induction-machine stages; on the generator side, regulation maintains DC-bus voltage and manages power sharing with the battery and loads [80,81]. Selecting the modeling and control stack is a trade-off between real-time performance and fidelity, with the goal of improving dynamic response while preserving stability under hybrid power-split operation.

(5) Power-conditioning unit modeling: Hybrid powertrains use several power-conditioning units to connect engine-driven generators, batteries, and distributed loads, so tractable models of AC/DC rectifiers, DC/DC converters, and DC/AC inverters are essential. For AC/DC rectifiers, physics-based models from power electronics and electromagnetics resolve device switching and network dynamics with high fidelity. Reduced or averaged models trade detail for speed. Synchronous reference-frame (dq) formulations and circuit-dq transforms give time-invariant averaged models for three-phase PWM rectifiers and support controller synthesis and small-signal studies; when device detail is unnecessary, these dq/averaged models scale well for system work. Data-driven identification is useful when hardware parameters are uncertain, but it requires care to avoid overfitting. See [82,83] for representative dq/circuit analyses, averaged/small-signal models, and predictive control examples.

For DC/DC converters, several model families are available. Exact switch-level models capture device stress and switching loss but are computationally heavy. State-space averaging and its extensions—generalized averaging, switching-frequency-dependent averaging, and the PWM-switch model—yield low-order, control-oriented dynamics suitable for compensation and stability design. When ripple coupling and spectral content matter, harmonic state-space or dynamic-phasor models retain selected harmonics while remaining far cheaper than full EMT simulation. Data-driven surrogates, from classical identification to ML-based fits, can speed parameterization or emulate parasitics if trained with sufficiently rich excitation. Foundational references include the Middlebrook–Ćuk framework, generalized/dynamic-phasor methods, switching-frequency-dependent and PWM-switch models, and recent HSS treatments [84,85,86].

For DC/AC inverters that drive propulsion machines or connect the DC bus to AC subsystems, dq models derived with Clark/Park transforms underpin most current- and voltage-loop designs and grid-interactive control. dq small-signal models enable impedance-based stability analysis (e.g., Sun’s criterion) and multi-converter interaction studies, while harmonic state-space or dynamic-phasor models address weak-grid coupling and cross-frequency effects. When modules are vendor “black boxes,” data-driven models provide a pragmatic route for tuning and interaction studies. Surveys and tutorials on dq control, microgrid/VSC control structures, impedance-based stability, and harmonic/dq modeling offer established foundations [87,88,89,90].

The choice among these models should be guided by the study objective, whether it is device-level electro-thermal design, control co-design, or system-level energy management, as well as by bandwidth and accuracy requirements and the availability of data. In practice, hybrid workflows that combine a physics-based backbone with identified parameters or spectral (dynamic-phasor) extensions often provide the best balance between fidelity and complexity for hybrid-electric aircraft systems.

Against this backdrop, salient divergences between aerospace and automotive contexts motivate the comparative matrix in

Table 4. Comparative matrix of modeling approaches in aerospace vs. automotive hybrid systems.

Modeling Approach	Typical Fidelity & Scope	Automotive Suitability	Aerospace Suitability	Aviation-Specific Blockers/Required Adaptations
0D/1D lumped electro-thermal (cells, bus, engine-gen)	Fast, low-CPU; limited spatial gradients	✓	△	Requires conservative margins for DO-160 environments; needs traceability for thermal derating and aging across long missions
Grey-box (physics + identified params)	Balanced fidelity; identifiable	✓	✓	Parameter identification must cover hot-high, icing, turbulence; evidence for extrapolation beyond test points
Surrogate/meta-models (RSM, GP, NN)	Very fast once trained; opaque	✓	△	Must demonstrate bounded error and explainability; runtime monitors or envelopes to ensure policy stays in training domain
High-fidelity electro-thermal–mechanical co-models (multi-domain)	Accurate; CPU-intensive	△	✓	Acceptable for offline design/certification evidence; for onboard use, needs reduced-order models with verified error bounds
CFD/FEA-in-the-loop	Highest fidelity; non-real time	×	△	Not for onboard EMS; only for design substantiation and offline envelope generation
Aging/SOH coupled battery-generator models	Degradation and lifecycle captured	△	✓	Required for dispatch reliability; must tie to maintenance intervals/MEL and health-monitoring evidence
Uncertainty-aware/envelope models	Worst-case + robustness	△	✓	Needed for DAL-level safety targets; used to generate certifiable constraints for controllers

(✓ = well-suited; △ = conditionally viable/with adaptations; × = generally impractical).

.

Road-vehicle modeling often optimizes cycle-average efficiency and calibration effort, so fast surrogates with limited explainability can be acceptable; in aerospace, flight safety and prospective certification shift the emphasis toward models that carry electro-thermal aging and environmental extremes, provide traceable error bounds for reduced-order forms used onboard, and link parameters to inspection and maintenance evidence. For flight implementation, the practical rule is to favor the simplest model that can meet deterministic avionics timing with bounded memory, expose safety-critical states and envelopes (SOC, bus voltage, temperature, torque–speed), and support requirement-to-test traceability; high-fidelity multiphysics remains valuable offline for envelope derivation and evidence, while black-box surrogates are used only when training domains, extrapolation limits, and runtime monitors are explicitly documented.

3. Energy Management Strategy: Control Algorithm

Modern hybrid aircraft pair a gas turbine with one or more electric drives and onboard sources such as batteries, supercapacitors, or fuel cells. More sources raise peak capability but also make energy allocation harder [91]. Taking the turbo-electric hybrid system as an example, the energy-management strategy (EMS; Figure 8) has moved from a peripheral function to a mission-critical discipline. It sets the instantaneous power split over a flight mission [92,93]. A good EMS should

• Enforce primary flight-mechanics constraints (altitude, speed, attitude);
• Minimize secondary costs (fuel burn, emissions, thermal stress et al.);
• Suppress high-frequency power ripple that shortens component life;
• Satisfy device limits (battery C-rate, motor temperature, SOC et al.);
• Run in real time on embedded hardware with tight computational budgets.

The EMS in a hybrid powertrain coordinates power split, battery supervision, reliability assurance, and control tuning. Typical objectives combine economy (unit efficiency and fuel consumption), durability (degradation of the power sources), and multi-objective cost or loss functions, while ensuring the load receives the commanded power [94,95]. Prior surveys group methods into three families: rule-based, optimization-based, and learning-based. But the boundaries are often porous, and practical schemes mix elements of two or even all three [96,97,98].

Table 5. Advantages and disadvantages of various EMS methods.

Categories	Method	Techniques	Advantages	Disadvantages
Rule-Based Control Strategies	Deterministic Rule-based	- State machine control - Power-following control	- Simple structure, easy implementation - Low computational load, real-time performance - Robust, suitable for practical applications	- Moderate control accuracy, non-optimal solution - Poor adaptability to complex conditions - Heavily relies on empirical tuning
	Fuzzy Logic-based	- Fuzzy logic control - Adaptive fuzzy control	- No need for precise mathematical models - High flexibility, able to handle uncertainties - Adaptive capability to varying conditions	- Complex parameter and rule design, requiring expert knowledge - Performance limited by quality of designed rules, potentially suboptimal
Optimization-Based Control Strategies	Global Optimization	- Dynamic Programming (DP) - Pontryagin’s Minimum Principle (PMP) - Evolutionary Algorithms	- Guaranteed global optimal solutions (theoretically) - High control accuracy, suitable as benchmark - Useful for evaluating other methods	- Extremely high computational complexity, usually offline only - Requires complete knowledge of the mission profile, poor real-time applicability in engineering
	Real-time Optimization	- Model Predictive Control (MPC) - Equivalent Consumption Minimization Strategy (ECMS)	- Real-time applicability, suitable for online implementation - Solutions close to optimal under real-time constraints - Good adaptability to varying operational and environmental conditions	- Higher computational complexity compared to rule-based strategies - Highly dependent on prediction accuracy and quality of predictive model - Still possibly suboptimal
Learning-Based Control Strategy	Learning-based	- Reinforcement Learning (RL)	- Autonomous learning without explicit modeling required - High adaptability and continuously improvable - Effective in handling complex and dynamic scenarios	- Requires extensive data and long training periods - High computational resource demand during initial training phase - Control performance stability depends heavily on the quality of training

lists representative algorithms in each family and summarizes their main strengths and limitations.

Against this backdrop, EMS for flight must be posed under aviation constraints: hard safety envelopes on SOC, bus voltage and temperature, torque–speed and power-quality; tolerance to sensor dropouts and component derating; and implementation that is deterministic in timing with bounded compute and interpretable logic on avionics-grade hardware. These requirements shape method choice: rule-based schemes remain attractive at early TRL and for HIL due to transparency; optimization-based ECMS/MPC provide explicit constraint handling with verifiable runtimes; learning-based methods are viable only when confined to safe-RL patterns with action filtering, runtime monitors, and a certified supervisory shell. In practice, a certifiable baseline uses rule-based envelopes or convex QP-MPC as the supervisor, with ECMS recovering local efficiency within verified limits; where adaptability is needed, a filtered learning advisory operates strictly inside the enforced envelopes. Unconstrained model-free RL or in-flight online adaptation is generally unsuitable without strong safety guards and timing guarantees. In the subsections that follow, each family is evaluated not only by mission-economy metrics but also by its ability to enforce safety envelopes, accommodate faults, and meet certification-friendly implementation criteria.

The applicability of control algorithms in aerospace systems differs somewhat from that in the automotive industry, as shown in

Table 6. Comparative matrix of EMS methods in aerospace vs. automotive sectors.

EMS Method	Real-Time and Determinism	Constraint Handling	Explainability	Automotive	Aerospace	Why Impractical/How to Adapt for Aviation
Rule-based/heuristics	Hard real-time	Explicit by design	High	✓	✓	Baseline for early TRL/HIL; scales poorly to multi-physics unless structured with envelopes
ECMS (Equivalent Cons. Min.)	Real-time capable	Soft via penalties; can add hard bounds	Medium	✓	✓	Works if penalties are certified with margins; needs envelope guards for thermal/SOC hard limits
DP (global offline) + policy tables	Offline global optimal; lookup online	Constraints baked in	High	✓	△	Online DP is ×; offline DP OK for table generation; requires interpolation guards and coverage analysis
MPC (QP/NLP)	Deterministic if QP	Hard constraints natural	Medium	✓	✓	Preferred for certifiable runtime if convex; for NLP needs proof of timing bounds or fallback to QP
Model-free RL (DQN/TD3/PPO)	Non-deterministic by default	Implicit	Low	✓	×	Impractical without safety shields, action filters, and timing guarantees; black-box nature blocks certification
Safe-RL (constrained RL, shields, Lyapunov/CBF layers)	Near real-time if small nets	Hard/soft via safety layer	Medium	△	△/✓	Conditionally viable with a certifiable supervisory shell + monitors; policy size and timing must be bounded
Hybrid supervisory: MPC/ECMS outer + RL inner (advisory)	Deterministic outer loop	Hard via outer; RL proposals filtered	Medium-High	△	✓	Recommended path: outer layer enforces safety/traceability; RL only proposes within a certifiable envelope
Online learning/adaptation	May violate timing	Risk to constraints	Low	△	×	Disallowed unless adaptation is bounded, logged, and reverted on anomalies; typically performed on ground, not in flight

(✓ = well-suited; △ = conditionally viable/with adaptations; × = generally impractical).

.

Aviation programs must exclude methods that lack deterministic timing, bounded compute, or explainable decisions, since unconstrained model-free RL or in-flight online adaptation without hard-constraint guarantees is generally impractical for certification and dispatch reliability. A workable trajectory is a hybrid supervisory pattern in which a certifiable outer controller such as rule-based envelopes, ECMS with hard limits, or convex QP-MPC to enforces safety and timing, while a filtered learning advisory contributes efficiency strictly inside monitored action bounds. Fault tolerance and reconfiguration are integral: the supervisor detects and isolates sensor dropouts and component derating, enters predefined degraded modes, and reallocates power to keep bus voltage, SOC and temperature margins, and torque–speed envelopes within limits, preserving limp-home capability. This framing positions the families as follows: rules provide transparency at early TRL and for HIL. ECMS, and QP-MPC, handle constraints with a predictable runtime and learning are appropriate only as an advisory inside certified envelopes with runtime monitors.

3.1. Rule-Based Methods

Rule-based EMS relies on expert knowledge and mission experience to schedule sources with conditional logic (if–then rules). The structure is explicit and easy to debug, which suits early prototyping and applications with tight real-time constraints. According to whether the rule thresholds are crisp or fuzzy, strategies fall into two groups: deterministic and fuzzy.

3.1.1. Deterministic Rules

The finite-state machine (FSM) is the core deterministic approach and is widely used on small hybrid UAVs. As sketched in Figure 9, state variables such as SOC, motor power demand, and throttle command drive transitions among predefined modes, which govern energy flow and source switching [99]. In this setting, rule design often targets fuel-cell safety, efficiency, and lifetime [100]. Building on the basic FSM, Jin et al. added a voltage-hysteresis controller to improve cold-start performance in a fuel-cell/battery system [101]. Other FSM variants keep SOC within bands (e.g., 45–65% in flight and 40–60% at mission end) to control cost and extend life [102,103]. Owing to their simplicity and robustness, such deterministic schemes remain common in fuel-cell/battery/supercapacitor hybrids.

FSMs are attractive because they are simple and respond quickly. Their weak points are limited ability to represent complex situations and a heavy dependence on hand-crafted rules, which can hurt performance in dynamic or diverse missions. To mitigate this, Li et al. [104] combined an FSM with the Equivalent Consumption Minimization Strategy (ECMS): the FSM selects the operating mode, and ECMS then allocates power locally optimally. This pairing keeps the logic transparent while improving fuel economy.

Power-following (PF) is another deterministic scheme used when hybrid UAVs must track fast, time-varying loads. The controller estimates the instantaneous propulsion-power demand and splits it between engine and motor using simple algebraic rules. Because PF relies only on the current load and predefined limits, it is model-free and computationally light. Its drawback is the lack of global optimization: it does not explicitly minimize fuel consumption or battery aging over a mission. Figure 10 illustrates an example that combines PF with an FSM.

Other deterministic rules are also used. The stiffness-coefficient model control adjusts the battery’s charge/discharge coefficients as a function of state of charge to curb fuel use [105]. The operating-mode model control assigns a reference power based on load demand and battery status, although its effectiveness depends strongly on the engineer’s tuning and experience [106].

In summary, deterministic rule-based supervisors such as FSM and power-following are reliable, explainable, and run in real time on low-power avionics, which suits early prototypes and cost-constrained UAVs. Their weakness is adaptability and scalability when multiphysics coupling is strong or missions drift from the assumptions baked into fixed thresholds. For flight use, codify SOC/voltage/temperature bands and torque–speed envelopes as hard guards, add hysteresis and dead-bands to prevent chattering, document coverage against the operational envelope, and, where efficiency matters, layer ECMS within the same certified structure to recover local optimality without sacrificing transparency.

3.1.2. Fuzzy Rules

As hybrid fuel–electric powertrains add sources and couplings, hand-crafted state machines become hard to design and brittle to operate. Fuzzy logic control (FLC) was introduced to relieve this burden. Instead of crisp, deterministic thresholds, FLC uses fuzzy rules and membership functions, which improves robustness and allows energy allocation to be computed from a fuzzy inference process [107].

In practice, FLC fuzzifies selected inputs (for example, SOC, its rate of change, and the instantaneous power gap), applies a rule base through an inference engine, and then defuzzifies the result to produce control commands. This structure handles nonlinear behavior, large power swings, and frequent load changes and typically yields smoother actions under uncertainty. A representative workflow is shown in Figure 11.

To raise adaptability beyond hard rules, fuzzy logic is often combined with rule-based frameworks or simple optimizers. One online fuzzy finite-state-machine EMS for a fuel-cell/photovoltaic/battery UAV, for instance, delegates PV–battery flow to the state machine while a fuzzy layer allocates fuel-cell and battery power; mission-level simulations report gains over thermostatic control [108]. Pure fuzzy-rule control strategies have also shown faster responses and stronger robustness than conventional state-machine control in comparable settings [109].

FLC still requires careful design of membership functions and rule bases, and it offers no global optimality guarantee, but its balance of simplicity and robustness makes it a practical step up from deterministic rules in many hybrid UAV applications.

Adaptive fuzzy control (AFC) builds on a static FLC by updating membership functions, rule weights, or both as operating conditions change or components age. In practice, AFC improves economy and durability in real time, as shown by Zhang et al. [110]. Adaptive neuro-fuzzy inference systems (ANFIS) and related compensatory fuzzy–neural schemes further enhance resilience under variable loads [111].

Because membership functions and rule bases are still chosen by hand, metaheuristic optimizers including genetic algorithms (GA) [112], particle-swarm optimization (PSO) [113], and bee algorithms (BA) [114] are often used to automate tuning [115]. A PSO-aided fuzzy controller for a fuel-cell/battery hybrid, validated on a 30 min mission and in rapid-control-prototype tests, showed markedly better tolerance to power fluctuations than classical rules or untuned fuzzy logic [116].

In summary, Classical FLC provides a low-cost, interpretable baseline for hybrid-aircraft EMS, and adaptive-fuzzy control adds online adjustment that tracks aging and mission changes without violating real-time budgets; yet both rely on well-designed initial rules and rigorous validation, lack global optimality, and remain expert-dependent. To make these schemes flight-ready, automate membership and rule tuning with constrained searches under certified bounds, hard-limit outputs using the same supervisory envelopes as rule-based control, and demonstrate worst-case timing determinism on the target avionics.

3.2. Optimization-Based Methods

Optimization-based EMS poses power-split control as an optimal-control problem. A weighted objective, typically including fuel consumption, emissions, and battery-degradation cost, with optional penalties for noise or thermal effects, is minimized subject to algebraic and differential constraints that represent the propulsion architecture and the flight envelope. Solving the program with the plant model in the loop enforces the true electro-mechanical dynamics and explicit actuator limits that rule-based schemes only approximate. In practice, the methods are divided into global and real-time methods: the former is computationally heavy and mainly used offline; the latter seeks near-optimal decisions on embedded hardware with limited foresight and compute.

Global methods such as DP and PMP serve as offline gold standards for benchmarking, envelope construction, and table generation but are rarely suitable onboard due to memory, forecast, and determinism requirements. Real-time control schemes, such as convex QP-MPC with explicit hard constraints or ECMS with carefully calibrated penalties and envelope safeguards, can achieve certifiable timing on embedded processors. This is feasible provided that solver parameters are fixed in advance, the worst-case iteration time does not exceed the control period, and reliable fallback mechanisms are available in cases of saturation or infeasibility.

3.2.1. Global Optimization

Dynamic programming (DP) breaks a multistage decision problem into subproblems and constructs the optimal policy by backward recursion. In hybrid-electric aircraft studies, DP is widely used to establish best-case benchmarks and to generate high-quality training data for learning-based controllers. Its strength is exhaustive exploration of state–action grids, which guarantees global optimality for the chosen discretization (at the cost of significant computation). The optimality principle can be summarized as follows [117]:

Equation of state:

$$x_k=T_k\left(x_k,d_k\right)$$

(1)

Value function:

$$J=\mathrm{m}\mathrm{i}\mathrm{n}{\sum }_{k=0}^{n-1}{v}_k\left(x_k,d_k\right)$$

(2)

The optimal principle:

$$f\left(x_k\right)=opt\left\{v_k\left(x_k,d_k\right)+f_{k+1}\left(x_{k+1}\right)\right\},d_k\in D_k,k=n-1,n-2,\cdots ,0$$

(3)

A practical DP setup first defines discretization grids for the key states: state of charge (SOC), the flight-segment index, and any additional variables such as battery temperature or engine spool speed. With terminal conditions fixed at the mission end, the algorithm then computes the cost-to-go at each grid point by backward recursion to take-off. The result is a policy lookup table that maps every admissible state (e.g., segment, SOC, temperature) to the engine and motor power commands to request. The overall flow is illustrated in Figure 12.

Among these methods, DP remains a benchmark because it decomposes multi-stage decisions via Bellman’s optimality principle [118]. Standard DP, however, suffers from the well-known “curse of dimensionality” [119]. To alleviate this, researchers have developed adaptive DP (ADP) and stochastic DP (SDP) [120], as well as multi-dimensional DP for fuel-cell/battery/supercapacitor hybrids [121]. Fares et al. [122] further proposed a weighted DP that accelerates convergence and mitigates computation overhead.

Despite its rigor, DP faces two practical hurdles. First, it requires a full forecast of the mission profile, including altitude, airspeed, wind, and payload, before computation begins; any deviations in flight invalidate the precomputed policy. Second, its memory and CPU demands grow rapidly as grid resolution increases or as new states are added. Common mitigation strategies include using coarse-to-fine meshes, pruning unreachable states, and clustering similar states to reduce the size of the policy table without sacrificing fidelity.

Pontryagin’s Maximum Principle (PMP) is another powerful tool for global optimization [123]. Pontryagin’s Minimum Principle addresses the same optimal-control problem from a continuous-time perspective. Instead of scanning an entire grid, PMP derives necessary optimality conditions and then integrates a set of forward–backward differential equations until the prescribed boundary conditions are satisfied. This method therefore requires far less memory than DP and can operate with much finer resolution in states such as SOC or temperature.

PMP reformulates the original trajectory-optimization task as a series of instantaneous Hamiltonian minimization problems; when the resulting sequence of minima is unique under finite boundary conditions and constraints, the assembled trajectory is globally optimal. The definition of the objective function of the optimal control problem is defined as follows:

$$\begin{array}{c}\underset{u(\cdot )}{\mathrm{m}\mathrm{i}\mathrm{n}}Jx(\cdot ),u(\cdot )=Kx\left(t_f\right),t_f+{\int }_{t_0}^{t_f}Lx\left(t\right),u\left(t\right),tdt\\ \mathrm{s}.\mathrm{t}.\dot{x}\left(t\right)=fx\left(t\right),u\left(t\right),t,t\in [t_0,t_f]\\ x\left(t_0\right)=x_0,\\ x\left(t_f\right)=x_f\end{array}$$

(4)

where $J\left(x_t,u_t\right)$ refers to the objective function; $K\left(t_f\right)$ represents terminal constraints; $t_0$ and $t_f$ represent the initial moment and termination time; $L\left(x_t,u_t,t\right)$ represents the transition objective function; $x$, $u$, and $t$ denote the state variable, control variable, and time, respectively. Then, The Hamiltonian function is defined as follows [124]:

$$[Hx\left(t\right),u\left(t\right),\lambda \left(t\right),t=Lx\left(t\right),u\left(t\right),t+{\lambda }^T(t\left)fx\left(t\right),u\left(t\right),t\right]$$

(5)

where $\lambda \left(t\right)$ is a co-state variable. Solving the Hamiltonian yields the optimal state trajectory and control law over the entire cycle. Dobrokhodov et al. [125] applied PMP to minimize mission energy in a UAV equipped with fuel cells and photovoltaic panels.

PMP has two main drawbacks. It assumes full knowledge of the mission profile in advance, and in non-convex problems it can settle at a local minimum. For these reasons, open-loop optima from DP or PMP are most often used as offline benchmarks to judge real-time strategies.

Accordingly, flight programs typically precompute policies and envelopes with DP/PMP offline while delegating online control to certifiable ECMS or QP-MPC that provably respects those envelopes.

In many EMS studies the objective is broader than fuel economy; component life and pollutant emissions also matter. Evolutionary algorithms suit such multi-objective settings.

In a genetic algorithm (GA), each candidate schedule is encoded as a chromosome. Genes can represent segment-wise engine and motor power levels, or a reduced set of switching instants and SOC targets. The algorithm starts with a population seeded randomly or with heuristics. Each generation selects the better candidates, applies crossover to mix their traits, and adds small mutations to explore new regions. With appropriate selection pressure and mutation rate, the population moves toward high-quality schedules while keeping enough diversity to avoid premature convergence. GA is robust to nonlinear models and strikes a clear balance between exploration and exploitation, but it requires many mission simulations to evaluate each new generation.

Many researchers have contributed to GA-based energy-management strategy research. Building on this evolutionary technique, the Nondominated Sorting Genetic Algorithm (NSGA) ranks individuals by dominance relations before selection, giving it strong multi-objective capability. The refined NSGA-II [126] improves computational speed and robustness through faster non-dominated sorting, a crowding-distance operator that preserves diversity, and an elitist strategy. Donateo et al. [127] later proposed a streamlined non-dominated sorting scheme that is even more computationally efficient. Applied to hybrid-power UAVs, NSGA-II reduces fuel consumption, an advantage for long-endurance missions [128]. Extending this line of work, Xie et al. [129] introduced a benchmark non-dominated sorting (BNDS) method, demonstrating that a hybrid UAV optimized with BNDS achieves lower fuel burn together with improved cruise and climb performance.

Particle Swarm optimization (PSO) treats each candidate schedule as a particle with a position and velocity in the search space. At every step the velocity is updated by three terms: inertia, attraction to the particle’s own best position, and attraction to the swarm’s best position. This coupling pulls particles toward good regions while still allowing exploration. PSO is easy to implement (only an inertia weight and two acceleration coefficients) and it often converges quickly when the cost surface is smooth. In rugged landscapes, it can stagnate; scheduling the inertia weight or adding random perturbations helps.

In EMS studies, PSO typically starts from a randomly initialized swarm. Each particle evaluates fitness, stores its personal best, reads the global best, and then updates its state accordingly. As shown in Figure 13, PSO and GA differ in memory and operators [130]: PSO retains earlier improvements through personal and global bests, while GA may discard them during crossover and mutation. PSO also avoids crossover and mutation entirely, which yields a leaner rule set and can shorten convergence. These properties explain its use in function minimization, feed-forward neural-network design, and multi-objective, multi-constraint optimization [131]. Hybrids are common: Juang et al. combined GA and PSO (GAPSO) and reported better search performance than either method alone [132].

The Bat Algorithm and Simulated Annealing also appear in EMS work, usually as lightweight alternatives or as post-processing refiners rather than primary optimisers.

Taken together, DP provides a true global optimum by exhaustive search, PMP supplies optimal switching structure through necessary conditions, and evolutionary methods such as GA and PSO approximate the optimum in complex nonlinear models through population-based exploration. These approaches form a complementary toolkit for offline global optimization.

3.2.2. Real-Time Optimization

The equivalent consumption minimization strategy (ECMS) was first developed for conventional gasoline–electric hybrids. In that setting the engine supplies most of the energy, and the battery acts as a buffer that shaves peaks and fills valleys. ECMS converts the motor’s electrical power into an “equivalent” fuel rate through an equivalence factor that is adjusted online to keep the battery state of charge near its target window. At each control step, the strategy forms an instantaneous cost, defined as the sum of the engine’s actual fuel flow and the motor’s equivalent fuel flow, and then selects the power split that minimizes this cost subject to actuator limits. In effect, the original global problem is replaced by a sequence of local minimizations that run in real time. The result is a simple controller that lowers total fuel use and associated emissions while maintaining SOC neutrality over the mission. A schematic of ECMS is given in Figure 14.

Equivalent Consumption Minimization Strategy (ECMS) has become the de facto real-time optimiser for extending UAV endurance and lowering hydrogen usage [133]. The instantaneous cost function aggregates not only the direct hydrogen flow but also the equivalent hydrogen associated with battery or super-capacitor power exchanges [134,135]. Consequently, the control objective is to drive this total equivalent consumption to a minimum at every sampling step [136].

Several researchers have refined the basic framework. Zeng et al. implemented an adaptive ECMS that employs an iterative-learning loop to approach near-optimal fuel use on-line [137]. A fuel-cell/battery/super-capacitor hybrid powertrain governed by ECMS was compared against a rule-based benchmark in [138]; the ECMS scheme lowered hydrogen demand and mitigated fuel-cell degradation by letting the battery provide mid-range support while the super-capacitor handled power peaks, provided that the super-capacitor state-of-charge is actively limited to avoid over- or under-charge.

Heuristic enhancements have also been explored. ECMS variants that embed the Salp Swarm Algorithm (SSA) [139], an External Energy Maximization Strategy (EEMS) [98], or the Mine-Blast Algorithm (MBA) [140] further sharpen fuel economy. In a systematic comparison of control policies for a fuel-cell/battery/super-capacitor system, Rezk et al. confirmed that the SSA-assisted ECMS delivered the highest overall efficiency and the lowest hydrogen consumption [141].

ECMS originates from Pontryagin’s Minimum Principle; therefore, its inherent limitations mirror those of PMP. When the powertrain is highly nonlinear, subject to stochastic disturbances, or required to satisfy multiple conflicting objectives in real time, ECMS may no longer be adequate. For instance, designing an EMS for an aircraft operating in severe atmospheric turbulence involves strong, random external perturbations that greatly increase system nonlinearity, making a classical ECMS formulation intractable.

Model predictive control (MPC) is a flexible framework for linear and nonlinear dynamics in hybrid powertrains. Current work focuses on three architectures: decentralized MPC, hierarchical distributed MPC, and fully distributed MPC [142,143,144]. In a decentralized scheme, several local controllers run in parallel. This partitioning lowers computation and improves scalability and fault tolerance, but residual coupling among subsystems can still threaten closed-loop stability. A hierarchical distributed design adds a supervisory layer that gathers system-wide information while local controllers pursue their own objectives; coordination improves, yet extensibility suffers when new modules must be added. A fully distributed scheme pushes modularity further: each subsystem solves its own problem and exchanges limited information with neighbors. The design scales well and is robust, though performance may drop when inter-subsystem interactions are treated only approximately.

Figure 15 shows the standard MPC loop [145]. Compared with ECMS, MPC solves a short horizon optimization at each sampling instant, which keeps the computational load modest and supports real-time deployment. Applications include power-flow balance between fuel cells and supercapacitors [146]. Chen et al. embedded a fuzzy-clustering model in a constrained MPC and showed that fuel-cell power can be allocated prudently, avoiding oxygen starvation in the stack [147]. The main caveat is model mismatch: uncertainty and disturbances can erode closed-loop performance, which limits MPC in demanding flight environments.

Beyond the main algorithms discussed earlier, several real-time control approaches have been adopted for power regulation in hybrid UAV powertrains (as shown in Figure 16), including game-theoretic (GT) control [148], proportional–integral (PI) control [149,150], sliding-mode control [151], and frequency decoupling (FD) [124].

3.3. Learning-Based Methods

EMS for hybrid propulsion systems must fuse heterogeneous data from sensors, propulsion subsystems, and mission profiles. Machine learning can extract patterns, build predictors, and support decisions, with reinforcement learning (RL) particularly suited to sequential control by learning a state–action policy that adapts to changing conditions. At the same time, certification concerns related to opaque decision pathways, incomplete coverage, and non-deterministic timing require that a viable aviation trajectory restrict the role of the learned policy to that of an advisory layer embedded within a certified supervisory framework. Such an approach relies on constrained or safety-oriented reinforcement learning constructs, including cost-bounded optimization, protective shielding mechanisms, or control barrier function and Lyapunov-based layers. In addition, it is necessary to impose limits on network size and inference time for the target hardware, to prohibit parameter updates during flight, and to incorporate monitoring mechanisms that can identify out-of-distribution states before control actions are executed.

3.3.1. Fundamentals of Reinforcement Learning

Reinforcement Learning (RL) is an algorithm that allows an agent to interact with its environment and adjust its strategy over time based on feedback, aiming to maximize the cumulative rewards. The RL framework is illustrated in Figure 17. RL problems can be modeled as Markov Decision Processes (MDPs), which provide a mathematical foundation for decision-making. The key components of the RL algorithm include the agent, the environment, the state, the action, the policy, the reward and return, and the value function [152].

In RL, the policy, denoted by $\pi \left(a\right|s_t)$, guides the agent in selecting actions at each state $s_t$. This policy serves as a probability density function, representing the likelihood of taking action $a^{\prime }$ in state $s_t$.

$$\pi \left(a^{\prime }\right|s_t)=P(A_t=a^{\prime }|S_t=s_t)$$

(6)

After selecting action $a_t$, the agent transitions to a new state, and the probability of reaching any state is defined by the state transition function:

$$p\left(s^{\prime }\right|s_t,a_t)=P(S_{t+1}=s^{\prime }|S_t=s_t,A_t=a_t)$$

(7)

The reward $R_t$ is the feedback the agent receives after performing an action, which helps assess the quality of that action. The return $U_t$, representing the total accumulated reward, is given by the following:

$$U_t=R_t+R_{t+1}+R_{t+2}+\cdots$$

(8)

To account for the fact that future rewards may not be as important as immediate ones, a discount factor $\gamma \in [0,1]$ is introduced. This redefines the return as follows:

$$U_t=R_t+\gamma R_{t+1}+{\gamma }^2{R}_{t+2}+\cdots ={\sum }_{k=0}^n{\gamma }^k{R}_{t+k}$$

(9)

The return $U_t$ depends on the actions and states over time and is inherently stochastic. To address this, the expected value is used to define the action-value function $Q_{\pi }(s_t,a_t)$ and the state-value function $V_{\pi }\left(s_t\right)$:

$$Q_{\pi }(s_t,a_t)=E\left(U_t\right|S_t=s_t,A_t=a_t)$$

(10)

$$V_{\pi }\left(s_t\right)=E\left(Q_{\pi }\right(s_t,A\left)\right)$$

(11)

Equation (10) represents the expected return when taking action $a_t$ in state $s_t$ under policy $\pi$, while Equation (11) represents the expected return from state $s_t$. The optimal policy ${\pi }^{\mathrm{*}}$, which maximizes the return, can be derived by solving the Bellman equation:

$$Q^{\mathrm{*}}(s_t,a_t)=\mathrm{m}\mathrm{a}\mathrm{x}{Q}_{\pi }(s_t,a_t)$$

(12)

$$V_{\pi }\left(s_t\right)=R_t+\gamma {\sum }_{s^{\prime }\in S}p\left(s^{\prime }\right|s_t,a_t\left)V_{\pi }\right(s_{t+1})$$

(13)

By solving the Bellman Equation (13), the optimal action-value function $Q^{\mathrm{*}}$ is obtained.

Reinforcement Learning (RL) enables the agent to learn by interacting with the environment, refining its strategy through experience. However, RL struggles with tasks involving high-dimensional input data. Classic RL algorithms can be categorized into value-based and policy-based methods, depending on whether the agent learns a value function $V_{\pi }$ or a policy function $\pi$. Recent advancements in RL integrate deep neural networks to approximate these functions, enabling RL to address high-dimensional and continuous action and state spaces, thus improving the effectiveness of solving real-world problems.

The basic principle of value-based Deep Reinforcement Learning (DRL) involves using deep neural networks to approximate the value function for state-action pairs. A notable implementation of this approach is the Deep Q Network (DQN), introduced by Mnih et al. [153]. DQN applies Convolutional Neural Networks (CNNs) from deep learning to reinforcement learning, marking the inception of DRL research. The DQN framework is shown in Figure 18.

Q-Learning, a classic value-based algorithm, approximates the action-value function $Q^{\mathrm{*}}(s,a)$ by maintaining a Q-table for each state. While Q-Learning is effective in low-dimensional spaces, it becomes impractical in high-dimensional tasks due to the curse of dimensionality. DQN overcomes this limitation by using neural networks to approximate $Q^{\mathrm{*}}(s,a)$, allowing it to scale to high-dimensional data. The network is updated using gradient descent, and the introduction of an experience replay mechanism helps optimize learning by decoupling the correlation between sequential samples.

Deep Q-Networks (DQN) introduced two practical ideas follows: an experience-replay buffer that stores past tuples (state, action, reward, next state) and is sampled randomly to break correlation, and a target network that is updated only periodically to steady the learning process. These changes improve data efficiency and stability. DQN still has limits: it does not handle continuous action spaces, and it can suffer from Q-value overestimation and occasional instability.

Several variants address these issues. Double DQN (DDQN) reduces overestimation by decoupling action selection from action evaluation [154]. Prioritized experience replay focuses updates on informative transitions, which speeds learning. Duel DQN estimates a state-value stream and an advantage stream separately, which improves stability and sample efficiency [155].

Policy-based deep RL offers another route, especially for high-dimensional continuous control. Instead of learning action values, it learns a policy that maps states to actions directly. The actor–critic framework by Silver et al. [156] led to the deterministic policy gradient (DPG). Deep DPG (DDPG) extends this idea with neural function approximators, replay, and target networks, and has become a standard baseline for continuous control [157]. For reference, the DDPG training loop is summarized in Figure 19.

DDPG uses two neural networks: an Actor network $\pi (s;\theta )$, which approximates the deterministic policy function, and a Critic network $Q(s,a;w)$, which evaluates the action-value function. The Actor network selects actions based on the policy, while the Critic network evaluates those actions and helps update the policy. The DDPG algorithm is well-suited for handling continuous state and action spaces but is sensitive to hyperparameters and may become stuck in local optima.

Recent advancements in policy-based DRL algorithms, such as Twin Delayed DDPG (TD3) [158], Proximal Policy Optimization (PPO) [159], and Soft Actor-Critic (SAC) [160], have further enhanced the stability, efficiency, and robustness of reinforcement learning. These algorithms have shown superior performance in various domains, including energy management.

In the context of energy management, innovative RL algorithms have been applied with significant success. Four key RL algorithms that have been utilized in energy management include:

(1)

Hierarchical Reinforcement Learning (Hierarchical RL): This approach decomposes complex problems into sub-problems, with a meta-controller issuing sub-goals for lower-level controllers. Jiang et al. [161] applied this method to energy management in microgrid systems, transforming sparse rewards into dense ones.

(2)

Safe Reinforcement Learning (Safe RL): Safe RL focuses on ensuring that the agent’s actions meet task requirements while adhering to safety constraints. Ma et al. [162] introduced a conservative penalty framework to balance reward and cost while maintaining safety, with additional safety checks proposed in [163].

(3)

Multi-Agent Reinforcement Learning (Multi-Agent RL): This approach adapts traditional RL algorithms to support multiple agents with independent evaluation and goal networks. Multi-agent RL has been successfully applied in energy management for hybrid electric vehicles, as demonstrated by [164]. Other algorithms, such as Q-Mix [165], MADDPG [166], and MAVEN [167], have been employed in swarm control and robotics.

(4)

Meta-Reinforcement Learning (Meta-RL): Meta-RL allows agents to adapt quickly to new tasks with minimal data. This technique has been applied in energy management systems (EMS) for transport vehicles, where power demand and operating conditions change frequently, enabling rapid adaptation to new scenarios [168].

3.3.2. Applications of Reinforcement Learning in EMS

This section unfolds its discussion from two perspectives:

(1)

Algorithmic perspective: Initially, this section reviews the evolution and applications of reinforcement learning (RL) algorithms in energy management strategies across diverse vehicles, illustrating how these algorithms have progressively advanced and improved in performance.

(2)

Domain-focused perspective: Subsequently, the discussion narrows to hybrid aerospace systems, thoroughly examining RL-based energy management strategies in two typical configurations: hydrogen fuel cell–lithium battery and turboshaft engine–generator–lithium battery hybrid systems.

From the algorithmic viewpoint, researchers have progressively employed various RL algorithms in different applications, including HEVs, special-purpose vehicles, tracked vehicles, railway trains, more-electric aircraft, and hybrid-electric aircraft. Examples include: DQL/DDPG-based strategies achieving 4–8.9% reductions in fuel consumption and 93.8% of dynamic programming performance [169]; multi-step Q-learning achieving 29% improvement in energy efficiency and 10.68% average energy savings [170]; Double Q-Learning (DQL) approaches demonstrating faster convergence, better fuel economy than traditional DQL, and 93.2% planning performance, while optimizing dynamic engine switching to minimize fuel consumption [22,171,172,173]; D3QN/DDPG significantly enhancing decision accuracy and inference speed [174]; and TD3 algorithms effectively maintaining superior SOC states across diverse flight conditions [175]. These algorithms typically construct state spaces based on SOC, power demand, and vehicle kinematic parameters (such as speed, acceleration, engine speed, flight time), and optimize energy management through discrete or continuous control actions, including engine power outputs, throttle openings, gear shifting, and electrical switching. Moreover, their reward functions often revolve around fuel consumption and SOC deviation, with some studies additionally integrating efficiency curves, safety constraints, and battery lifespan considerations, significantly enhancing fuel economy, convergence, energy efficiency, and real-time control performance.

Subsequently, more advanced RL algorithms have emerged in energy management research. For instance, in mechanically parallel HEVs, a hierarchical actor-critic-based ACC-EMS strategy uses speed, position, SOC, and remaining fuel as states, with engine speed and electromechanical torque as actions, effectively reducing additional energy consumption caused by speed fluctuations and enhancing overall efficiency through hierarchical decision-making [176]. Similarly, a hierarchical DDPG method utilizes power demand and SOC deviation as states and rewards, automatically tuning heuristic control parameters and demonstrating near-DP fuel consumption performance and superior adaptability to varying driving conditions [177]. In electrical parallel systems, multi-agent IQL methods optimize individual fuel cell outputs using distributed control, demonstrating superior fuel economy and resilience in single-stack failure scenarios [164]; Nash equilibrium-based multi-agent Q-learning further improves convergence and global performance compared to single-agent and DP methods [178]; Distributed PPO with safety constraints demonstrates robust performance via simulations [179]; Additionally, Meta-RL combined with PPO rapidly achieves convergence across driving cycles with minimal training [168]. Figure 20 illustrates the developmental trajectory of energy management system (EMS) algorithms, progressing from rule-based approaches to global optimization, then to real-time optimization, and finally to reinforcement learning. The horizontal axis represents the timeline, and the vertical axis denotes the methodological progression of algorithms. To distinguish algorithm categories, we use different colors: blue for rule-based methods, yellow for optimization-based methods, and green for learning-based methods. Compared with conventional methods, reinforcement learning not only fulfills real-time requirements but also pursues optimality in dynamic operational environments.

Subsequently, we turn our attention to the application of reinforcement learning within hybrid-electric aircraft systems. As described in Chapter 2, typical hybrid-electric aircraft configurations can be classified into two categories based on the primary energy sources: fuel cell–battery systems and engine–battery systems. Although these configurations differ in hardware architecture, their energy management strategies share the common objective of efficient energy flow allocation.

To date, reinforcement learning has been extensively employed in the study of energy management strategies for hybrid-electric aircraft.

Table 7. Advances in EMS for Aerospace Hybrid Systems.

Type	Components	Strategies	Remark	Ref.
FC hybrid configuration	FC/BS/SC	SM, FL, PI, ECMS	Simulation only	[98]
FC hybrid configuration	FC/BS	Online fuzzy energy management	Simulation only	[110]
FC hybrid configuration	FC/SC	PI, PID-PWM	Experiment & simulation	[150]
FC hybrid configuration	FC/S	PMP	Experiment & simulation	[125]
FC hybrid configuration	FC/BS/SC	MBA, SSA	Simulation only	[141]
FC hybrid configuration	FC/BS/SC	Customization strategies based on electronic control units	Simulation only	[180]
FC hybrid configuration	FC/BS/S	Rule based	Experiment & simulation	[181]
FC hybrid configuration d	FC/SC	MPC, Rule based	Experiment & simulation	[146]
FC hybrid configuration	FC/BS	DP, Sequential Quadratic Programming	Simulation only	[182]
FC hybrid configuration	FC/BS	PMP	Experiment & simulation	[183]
FC hybrid configuration	FC/BS	FL, PSO-FL	Experiment & simulation	[184]
FC hybrid configuration	FC/BS	MPC, LOMPC	Experiment & simulation	[185]
Engine hybrid configuration	T/BS	MPC	Simulation only	[186]
Engine hybrid configuration	T/BS	MPC	Simulation only	[187]
FC hybrid configuration	FC/BS	DP	Simulation only	[188]
Engine hybrid configuration	E/BS	Q-Learning, Power Tracking	Simulation only	[189]
FC hybrid configuration	FC/BS	Rule based	Simulation only	[190]
Engine hybrid configuration	E/BS	Double Q-Learning	Simulation only	[22]
Engine hybrid configuration	T/BS	NSGA-II	Simulation only	[191]
Engine hybrid configuration	T/BS	TD3	Simulation only	[192]
Engine hybrid configuration	T/BS	PMP	Experiment & simulation	[193]
Engine hybrid configuration	T/BS	DDPG	Simulation only	[194]
Engine hybrid configuration	T/BS	Fuzzy-A-ECMS	Simulation only	[195]
Engine hybrid configuration	T/BS	Heuristic DP	Experiment & simulation	[196]
Other hybrid configuration	E/FC/BS/SC	diffusion-based distributed optimization, decentralized droop control	Experiment & simulation	[197]
Engine hybrid configuration	T/BS	PPO	Experiment & simulation	[198]

Abbreviations (Components column)—FC refers to fuel cells; BS refers to batteries; SC refers to supercapacitors; S refers to solar cells; T refers to Aircraft engines (including turboshaft, turbofan, etc.); E refers to internal combustion engine. Abbreviations (Strategies column)—SM: State Machine; FL: Fuzzy Logic; PI: Proportional–Integral; PID-PWM: Proportional–Integral–Derivative with Pulse-Width Modulation; ECMS: Equivalent Consumption Minimization Strategy; PMP: Pontryagin’s Minimum Principle; DP: Dynamic Programming; MPC: Model Predictive Control; LOMPC: Learning-/Online Model Predictive Control; PSO-FL: Particle-Swarm-Optimized Fuzzy Logic; MBA: Modified Bees Algorithm; SSA: Salp Swarm Algorithm; Q-Learning: tabular/action-value reinforcement learning; Double Q Learning (DQL): double estimator Q-learning; NSGA-II: Non-dominated Sorting Genetic Algorithm II; TD3: Twin Delayed Deep Deterministic Policy Gradient; DDPG: Deep Deterministic Policy Gradient; PPO: Proximal Policy Optimization; Fuzzy-A-ECMS: Fuzzy-adapted ECMS.

summarizes the principal EMS algorithms applied to hybrid-electric aircraft systems, detailing the configuration type, hybridization components, specific algorithms, and whether the studies include experimental validation or are simulation-only.

Table 7 provides a comprehensive overview of the application of various EMS algorithms in hybrid-electric aircraft systems, organized by configuration type, component combination, specific strategy, and whether experimental validation or simulation-only studies were conducted. Firstly, both fuel cell–battery (FC/BS) and engine–battery (T/BS or E/BS) configurations have been extensively investigated in simulations, with an increasing number of studies incorporating experimental testbeds, particularly for model predictive control (MPC), dynamic programming (DP), and reinforcement learning techniques such as Q-Learning, DDPG, TD3, and PPO. Secondly, the algorithmic evolution reflected in the table aligns with the development trajectory depicted in Figure 20: initial emphasis on rule-based strategies, proportional–integral control (PI), and equivalent consumption minimization strategy (ECMS), followed by the adoption of global optimization (DP, PMP) and real-time optimization (MPC, LQMPC), and most recently the focus on reinforcement learning and hybrid intelligent methods (MBA, SSA, NSGA-II, and various Q-Learning variants) to balance real-time decision-making with global optimality. Moreover, the “Other hybrid configuration” entry highlights emerging trends in multi-source coordination and distributed droop control. Overall, Table 7 not only illustrates the diversification of methods and the gradual enhancement of validation approaches but also lays a solid foundation for subsequent comparative analyses of strategy performance and applicability.

4. Future Prospects: Key Energy Management Technologies

The energy management system is the “central nervous system” of a hybrid-electric aircraft and the principal enabler of performance gains. Here we look forward to the following promising research directions in hybrid energy management system in the future.

To guide the reader, the next subsections progress from demand prediction (Section 4.1) to multi-time-scale coordination (Section 4.2) and to thermal–energy coupling (Section 4.3); Section 4.4 and Section 4.5 then summarize a certifiable EMS baseline and concise prospects for configurations and modeling.

4.1. Real-Time Propulsive Power Prediction

To satisfy power demands across diverse low-altitude flight regimes, compensate in real time for environmental disturbances, and improve both energy-management efficiency and overall energy utilization, hybrid systems must actively allocate power among multiple sources. This, in turn, requires accurate, real-time prediction of propulsive power under dynamically changing flight conditions with complex information flows [199]. We propose to learn a demand-power prediction model from historical flight data (e.g., attitude, airspeed, altitude, payload) using neural networks, and to fuse it with contemporaneous flight-control sensor measurements (e.g., wind speed, ambient temperature). The fused model dynamically compensates for environmental effects and outputs real-time power-demand estimates that serve as inputs to the intelligent energy-management system (EMS).

4.2. Multi-Time-Scale Energy-Management and Control

Conventional strategies often suffer from ambiguously defined multi-objective formulations and insufficient treatment of components with disparate time constants. We therefore suggest a hierarchical, multi-time-scale cooperative control architecture [200,201]. All operational constraints required for stable hybrid operation are identified and formalized, and the EMS jointly optimizes multiple objectives, including total fuel/hydrogen consumption, constant-voltage DC-microgrid regulation (bus-voltage ripple), and battery state-of-charge (SOC) and state-of-health (SOH). A two-layer scheme is developed: The upper layer with low control rate (about 1~10 s) is used for energy-allocation and power-split decisions, and the lower layer (about 0.01~1 ms) with fast control rate is used for the regulation of electrical subsystems.

4.3. Thermal Energy-Coupled Management

Given the increased architectural complexity, hybrid systems require explicit modeling of thermal–energy interactions and thermal response mechanisms across subsystems. From a thermodynamic-cycle perspective, the objective is to optimize heat-sink allocation among subsystems and, in support of adaptive and highly integrated design, to tightly couple the control and electrical domains in order to develop fully integrated thermal management algorithms [202,203]. Unlike conventional gas-turbine propulsion, hybrid propulsion architectures must address not only the thermal control of the gas turbine but also the substantial heat-rejection requirements of high-power electrical machines and power electronics. To this end, thermal energy-coupled management methods for hybrid-electric propulsion system need development.

4.4. Certifiable EMS Baseline: Electro-Thermal–Health Coordination

A practical flight path is to employ ECMS with temperature-linked costs and hard guards, or convex QP-MPC that augments states with lumped electro-thermal dynamics, while keeping any learning component as an advisory inside a certified supervisory shell. The supervisor enforces SOC/voltage/temperature and torque–speed envelopes, bounds inference time and memory on target avionics, and is evidenced by MIL/SIL/HIL campaigns. The reduced-order electro-thermal aging models carry documented error bounds to keep timing deterministic and decisions traceable.

4.5. Prospective Configurations and Modeling

Configurations likely to mature first are parallel and series parallel. Series and turboelectric/distributed concepts progress where HVDC standards, fault isolation, and thermal margins are robust. On modeling, the emphasis is on validated reduced-order multi-physics that expose SOC/SOH, bus-voltage and thermal margins with documented error bounds for onboard use, while high-fidelity CFD/FEA supports offline envelope derivation and design substantiation; grey-box/physics-informed structures aid traceability, and surrogates are acceptable when training domains, monitors, and envelope guards are explicit.

5. Conclusions

This review has organized hybrid-electric propulsion in two parts: configuration and control, and has linked them through modeling choices that enable practical EMS design:

(1)

On the configuration side, parallel and blended layouts offer complementary benefits. The selection should be guided by mission power profiles, allowable electrification depth, and integration constraints such as mass, volume, and thermal headroom. System-level power-flow models remain indispensable for rapid trade studies and controller prototyping, while physics-based, multi-domain models are essential for identifying operability limits, electro-thermal bottlenecks, and certification-relevant dynamics.

(2)

On the control side, rule-based schemes (deterministic and fuzzy) provide robust baselines for low-power avionics but tend to saturate in complex, time-varying missions. Optimization-based methods can supply benchmark optima (DP/PMP) and near-optimal real-time policies (ECMS/MPC) when accurate models and predictions are available. Learning-based controllers, particularly safe reinforcement learning, show strong potential for adaptability under uncertainty, provided they are trained with representative mission data, constrained to ensure safety, and validated against high-fidelity plant models and experiments.

Looking ahead, three priorities emerge: first, high-accuracy, low-latency propulsive-power prediction by integrating historical trajectory data with onboard sensing; second, hierarchical, multi-time-scale EMS that coordinates slow energy allocation with fast electrical regulation while maintaining bus-voltage, SOC/SOH, thermal, and actuator constraints; third, thermal energy-coupled EMS that co-designs energy flow and heat-sink allocation across engines, electrical machines, and power electronics to ensure efficiency and reliability.

In summary, near-term research should prioritize parallel and series–parallel configurations, while series, turboelectric, and distributed concepts may become viable as standards and thermal margins continue to mature. A practical pathway from prototypes to systems suitable for flight can be established by combining validated reduced-order models with explicit aging and thermal interfaces, integrated into certifiable energy management system baselines. Within this framework, learning-based methods should be employed only in an advisory capacity. Progress in these areas, together with open benchmarks, HIL and flight validation, and clear pathways to assurance and certification, will be critical for enabling the transition from promising demonstrations to scalable hybrid UAV and eVTOL operations.