Power management of hybrid fuel cell fixed wing UAVs using a fuzzy reinforcement learning system optimized with meta-heuristic methods

Abstract

Unmanned aerial vehicles (UAVs) are increasingly being powered by fuel cells, which provide a zero-emission green energy source, improve endurance, and reduce charging/refuelling times. These gadgets are used for anything from aerial photography to military activities. By tackling two problems—power management (PM) of the resources and design optimization (DO) of a hybrid electric source (HES) made up of a fuel cell (FC) and a battery—this study seeks to increase endurance and energy efficiency. It is designed for a fixed-wing electric unmanned aerial vehicle (EUAV) and uses a novel method to lighten the drone. For hybrid electric drones, energy management techniques are crucial. Using fuzzy logic-based programming and Multi-Factor Reinforcement Learning (MFRL), we will apply a reinforcement learning system to regulate the drone’s fuel consumption between the fuel cell and the battery. The Harris Hawk Optimization (HHO) algorithm is used by DO to determine the fuel cell and battery’s maximum power and capacity in order to reduce resource use. In order to choose the best management system, this PMS will use the HHO method to optimize the MFRL parameters and membership functions in the fuzzy logic structure. We have considered the uncertainty that governs the drone’s mobility and the effect of variations in wind speed in order to produce a realistic model. In the fuzzy system, we have also incorporated the wind speed variable for the energy management problem. Through the use of a modelling platform that integrates the UAV and hybrid power system models with a Matlab tool, the proposed method is assessed and yields an 8% weight reduction, saving a total of 70.43 kJ of energy, which can extend the “endurance phase” by more than 30 min. Additionally, the proposed method reduces the amplitude of SoC fluctuations, saving up to 40% of FC energy and enabling the UAV to operate for longer missions.

Introduction

Aerial vehicles powered by fuel cells have been chosen as a strategic program to reduce carbon emissions in the transportation sector. These vehicles will be used in urban and intercity fleets to alleviate traffic congestion and improve the speed and efficiency of transportation for both people and goods. Compared to internal combustion engines, electric propulsion in small fixed-wing UAVs has several benefits, such as being cheap, efficient, reliable, reducing noise, and generating low heat^1–3. However, since the majority of electric drones are solely powered by batteries, one of the well-known drawbacks of these drones is their short endurance (less than an hour) for specialized applications^2,3. Because of their high specific energy, hydrogen fuel cells have piqued the interest of many researchers because they enable longer drone endurance while preserving the benefits of electric propulsion. Fuel cells were used to enhance the endurance of fixed-wing UAVs from 0.25 h to 48 h in the Hornet (made in 2003) and the Ion Tiger (released in 2013)⁴. The low power density and slow dynamics of FCs can be addressed by combining them with a battery or an ultra-large capacitor, which can provide power peaks during take-off, climb, and quick maneuvers⁵.

Fuel cells are an ideal source of power for long-duration UAVs because of their high energy density and high conversion efficiency. In contrast to traditional combustion engine generators, fuel cells provide electrical energy with minimal noise, heat, and pollution. Thus, developments in fuel cell technology are congruent with the movements toward environmentally conscious aviation and electric-powered planes^6–8. The mobility and dependability of UAVs can also be increased by a hybrid fuel cell fuel system that combines batteries with high power density ultra-capacitors (UC) to make up for the fuel cells’ subpar transient performance.

The vehicle and UAV both have two distinct modes of operation: automated and manual. Keep in mind that the two have distinct features regarding the characteristics of the power required for propulsion. Due to their independence in all flight phases, including take-off, climb, cruise, maximum speed, and landing, fixed-wing UAVs are ideal for fields that are typically out of sight⁹. Several studies have been carried out on autonomous aircraft flight, including one on finding the most energy-efficient take-off route for inclined aircraft¹⁰, another on optimizing the aircraft’s conceptual design and the take-off route simultaneously to maximize payload weight¹¹, and still another on finding the best take off route for a tilted rotor aircraft¹². Some studies cover the entire flight, from take-off to cruise and landing¹³.

At certain points throughout the cruise mode, the UAV’s peak power demand remains relatively constant, although the vehicle’s power requirement fluctuates widely. Compared to the cruise phase, the climb phase has a substantially higher power need for the UAV. Nevertheless, rather than doing research in flight, the present emphasis in the field is on software simulations and ground demonstrations pertaining to UAV EMS of hybrid power systems. Few basic energy management solutions have been effectively employed for UAV systems because of their complexity, which significantly limits their aerodynamics and flight control rules^14,15. For UAVs powered by fuel cells or batteries, there are two primary control system problems to overcome when designing an efficient energy management system:

• i)To maintain battery power within the permitted range and lessen fuel cell system stress, how can the operating efficiency of the fuel cell system be enhanced in various flying scenarios?
• ii)For the controller to react to the UAV’s power consumption in real time, how may the computational load of the nonlinear energy management optimization problem be lessened given the constraints of the internal controller’s CPU and memory configuration?
• iii)How can the variations in ROC and battery charging and discharging be minimized to reduce the likelihood of battery failure?

Adapting the system to flight operations in an outside environment is a significant issue in tackling the EMS problem in real-world scenarios. To train the suggested models, a comprehensive collection of local weather data and flying conditions is also needed. Consequently, a significant advancement in fixed-wing UAV energy consumption will be the use of energy management strategies in the face of environmental uncertainty. One of the traditional real-time EMSs is fuzzy logic control, whose computation is not dependent on an exact energy optimization model of the system. Designing a high-performance online EMS for the UAV’s fuel cell/battery hybrid power system is the goal of this research work. A mathematical modeller for a propeller-based UAV is first simulated using MATLAB software. Next, a fuzzy logic technique is used to optimize the design and energy management plan for a five-mode flight mission. Subsequently, a wild horse optimization (WHO) algorithm is developed to monitor the ideal thresholds of the primary membership functions of the fuzzy logic-based scheduling system. This algorithm aims to minimize hydrogen consumption while keeping the lowest dynamic load weight of power sources as its optimization goal. To achieve this, it redefines a form of equivalent hydrogen consumption with a penalty function. Lastly, to determine the viability and efficacy of the suggested energy management techniques for the UAV, a three-hour dynamic mission profile of the UAV is tested on the suggested real-time model platform under the uncertainty of wind speed and weather conditions. The following highlights this paper’s primary contributions to the field of study.

• (i)This study presents an EMS based on WHO-based optimal fuzzy logic approaches that take into account the fuel cell UAV’s power requirement during various flight phases where the UAV propulsion load power was assessed with flight dynamics. The fuel cell hybrid power system can employ the suggested energy management approach in practical settings thanks to the thorough model.
• (ii)Based on the simulation findings for the UAV power system, a number of distinct EMS strategies are compared, including fuzzy logic, manual method-based control, and WHO-based fuzzy logic.
• (iii)Using the Wild Horse optimization technique, the UAV’s optimal design is first implemented with the goal of lowering the drone’s weight and improving its flying efficiency.
• (iv)By taking into account the uncertainties in the wind speed for the flight path, environmental factors such as variations in wind speed are taken into account in this energy management. Our analytical results show the effectiveness of the WHO fuzzy logic algorithm, the benefits of the energy management strategy, and the advantages of flexible demands to increase the UAVs’ flight range both with and without taking wind speed into account.

In this regard, the determined optimal design is essential to enhance the performance of such a hybrid power system in order to increase the size and PMS for fixed-wing UAVs using fuzzy time scheduling in energy resources. To execute an ideal measurement method for HES, the optimal design algorithm examined in this research makes use of the fixed-wing UAV characteristics and total mission power specifications provided in papers^4,16–18. Also, this study presents WHO-FL-PMs, a power management system (PMS) for fuel cell and battery hybrid sources that can protect the expensive fuel cell (FC) and avoid cell oscillation failure caused by extreme charging and discharging fluctuations.

To increase flight endurance and energy efficiency under environmental uncertainty, such as wind speed variations, this study explores the difficulties of energy management and design optimization in UAVs with a hybrid power system based on fuel cell and battery. The main issue in the design and operation of these UAVs is the optimal allocation of power between the fuel cell and battery during different flight phases (such as takeoff, cruise, endurance, maximum speed, and landing), while reducing the system weight, minimizing battery state of charge (SoC) fluctuations, and limiting the fuel cell response to sudden power changes. The development of an effective energy management system (EMS) is hampered by the computational complexity of real-time optimization, the constraints of UAV computational resources, and the impact of environmental variables like wind speed. The goal of this research is to develop a fuzzy logic-based reinforcement learning (MFRL) system optimized with the HHO algorithm that can reduce energy consumption by up to 105.43 kJ, reduce system weight by up to 8%, and increase flight endurance by up to 45 min while being flexible enough to adjust to changing environmental conditions.

In light of the aforementioned circumstances, this work suggests a novel approach to the design and energy management of propeller-motor-driven fixed-wing UAVs with the goal of minimizing the multi-objective function of an UAV. Design and energy management considerations for this approach stem from an optimization issue with uneven constraints on the multi-objective function, which takes into account uncertainties in wind speed throughout the flight route. For the suggested technique to work, it is necessary to have accurate information about the fixed-wing UAV’s aerodynamic and thrust properties beforehand. Understanding the UAV’s structure and environmental parameters is crucial since a rapid turn and climb will cause a stall in a real flight situation if the aerodynamic characteristics are unclear. Fixed-wing UAVs are frequently propelled by propeller engines since they are less expensive and simpler to use than jet engines. However, because fixed-wing UAVs’ airspeed varies, the thrust produced by propeller engines is calculated differently.

To improve endurance and energy efficiency, this work proposes an energy management system for a fuel cell-battery hybrid fixed-wing UAV based on multi-factor reinforcement learning (MFRL) and Harris Hawk optimization (HHO). The integration of swarm intelligence algorithms and adaption to various geographical situations are among the realistic and driven future plans for hardware implementation, real-world flight testing, and scalability. These plans are motivated by the need to validate the simulation results (e.g., 105.43 kJ energy savings and 45-min endurance increase) in real-world flight scenarios, which involve environmental complexities such as extreme changes in wind speed or temperature. Hardware implementation using power conversion modules (such as DC/DC converters, Section "System overview and modeling") and real flight tests to verify the robustness of the framework against environmental uncertainties (such as wind speed with an average of 5 m/s and a standard deviation of 2 m/s) are possible. Furthermore, the integration of swarm intelligence to optimize flight paths in diverse geographical environments, as proposed in this work, is strongly motivated with the aim of increasing the flexibility and practical application of the system in more complex missions, such as urban or intercity operations, although it requires additional computational resources and extensive validation.

The remainder of the document is structured as follows. Section "Literature review" provides a concise overview of previous research in the field. In Section "System overview and modeling", a case study in optimal design and energy management is presented, detailing the mathematical modelling of several UAV components applied to the aircraft throughout a flight mission. Part 4 lays out the issue statement, explains how to formulate optimization problems to extract design parameters, and delves into the fuzzy programming strategy for managing energy. Section "Results and discussion" details the outcomes of a three-hour flight mission simulation that was conducted to confirm the practicability of the parameters derived from the mass system analysis. The energy control mechanism that minimizes flight simulation energy usage is also detailed in this section. The investigation is finally concluded by providing the conclusions in Section "Results and discussion".

Literature review

Article¹⁹ introduces an energy-saving algorithm for positioning UAV-based base stations (UAV-BSs), taking wind effects into account. The goal is to reduce the propulsion power used by UAV-BSs while maintaining good communication with user equipment (UEs). It develops a new wind-influenced energy model and uses an ensemble learning method to optimize the 3D flight path, achieving a 47% reduction in energy consumption with minimal impact on UE capacity compared to existing methods.

Article²⁰ explores energy and trajectory optimization for hybrid electric fixed-wing UAVs powered by photovoltaic, fuel cells, or batteries, which are closely linked to flight dynamics. The study proposes a two-layer approach: an energy flight path optimization layer using a fuzzy neural network sequential convex optimization (FNNSCP) to maximize solar energy, and an energy management layer with quadratic convex MPC programming (CQPMPC) for power allocation. Simulations show FNNSCP cuts energy demand by 2% versus the Radau quasi-spectral technique (RPM), while CQPMPC reduces hydrogen use by 3.1% and 16.3% compared to nonlinear model predictive control (NMPC) and fuzzy logic state machine (FLSM), respectively, with overall savings of 5.2% and 15.6% in experiments.

Article²¹ presents a new optimization method to select the best power sources (supercapacitors, fuel cells, or batteries) for UAVs to lower operating costs. It includes an aerodynamic model covering four flight modes—forward motion, ascent, fall, and hover—and picks the optimal sources from a database based on mission needs, minimizing overall costs. Article²² focuses on boosting energy efficiency in hybrid electric UAVs by improving power allocation, reducing demand, and enhancing solar energy use. It creates a combined model for energy management and flight path optimization, solved with an adaptive sequential convex programming method (ASCP). This method, enhanced by a fuzzy-based trust region update and adaptive discretization, increases solar energy by 9.3% and 24.1% compared to Gauss pseudo-spectral technique (GPM) and uniform discretized sequential convex programming (UDSCP), respectively, with strong energy-saving results.

Article²³ investigates energy management and trajectory tracking for hybrid electric UAVs with solar panels, fuel cells, and batteries using a double-layer fuzzy adaptive nonlinear model predictive control (DFNMPC). The high-layer (H-FNMPC) optimizes solar energy gain for navigation, while the low-layer (L-FNMPC) manages power allocation to minimize hydrogen use. With flexible horizon adjustments and hydrogen flow rate calculations, DFNMPC saves 13.3% hydrogen on spiral paths and 56.9% on quadrilateral paths compared to a hierarchical fuzzy state machine. Article²⁴ proposes an adaptive hierarchical energy management approach (AHEMS) to improve efficiency in hybrid electric UAVs. It features an optimization layer that uses iterative convex optimization to set the battery SoC reference path, and a tracking layer with convex predictive control for real-time power allocation, fine-tuned by a fuzzy logic neural network. AHEMS enhances battery health and reduces hydrogen use, offering better energy management.

Article²⁵ addresses an optimal control problem for a hybrid UAV with a battery pack and generator in series. It develops a hybrid method starting with a mixed integer linear program (MILP) solution for the initial trajectory, solved using the nonlinear program solver IPOPT, to optimize the flight route and energy resource management. Article²⁶ suggests a fuzzy state machine (FSM) energy management strategy for a hybrid UAV using battery, fuel cell, and photovoltaic sources. The fuzzy logic handles fuel cell and battery power sharing, while a state machine manages photovoltaic and battery flow, combined in the FSM approach. Tested on a Matlab/Simulink platform, FSM outperforms a thermostat control strategy in fuel efficiency and power distribution, meeting mission demands effectively.

Slap Swarm Optimization (SSO) and Differential Flatness (DF) control are used in²⁷ to offer an optimal energy management strategy (EMS) for electric vehicles. In order to power a synchronous reluctance motor (SynRM)-based drive, the system uses hybrid battery-super capacitor power architecture. Each source is coupled in parallel to a DC bus via bidirectional DC-DC converters. The integration of SSO and DF’s complementing qualities is the strength of the suggested EMS. DF gains can be adjusted in real-time to improve system performance thanks to the SSO algorithm’s quick optimization process. In the meantime, DF ensures reliable control and adherence to dynamic resource restrictions by utilizing predetermined trajectories based on the physical parameters of the system. The EMS’s main goals are to maintain source dynamics, meet the power requirements of the SynRM motor, minimize DC bus voltage ripples (Δv = 5 V) and overvoltage of 15 V (3.2%), and stabilize the DC bus. The method also lowers battery current ripple by 17.15 A, increases battery cycle life, and decreases drive-induced harmonics by 10.49%.

An ideal EMS for a hybrid lithium-ion battery-super capacitor storage system that powers an electric car is presented in paper²⁸. A synchronous reluctance motor is powered by an inverter after the energy sources are linked in parallel to the DC bus via bidirectional DC-DC converters. The Bald Eagle Search (BES) algorithm and Fractional Order Integral Sliding Mode Control (FO-ISMC) are integrated by the EMS. The Urban Dynamometer Driving Schedule (UDDS) is used to assess the strategy’s efficacy. Metrics including voltage ripple, overshoot, and final battery SoC are used to compare the results with a traditional FO-ISMC-based EMS. The results show that the suggested EMS increases battery power consumption efficiency and improves power quality.

A novel parameter identification technique for electric vehicle (EV) applications using a Shepherd model and the Marine Predator Algorithm (MPA) is presented in Article²⁹. The method is verified under dynamic test settings, such as the Worldwide Harmonized Light Vehicle Test Procedure (WLTP), the New European Driving Cycle (NEDC), and the Urban Dynamic Driving Cycle (UDDC). With a voltage error of 2.743 × 10⁻³, a SoC error of 0.7693 × 10⁻³, and a root mean square error (RMSE) of 8.37 × 10⁻³ between the model and real data, the MPA-based approach achieves precise parameter identification, demonstrating its accuracy and robustness in capturing battery dynamics under real-world driving conditions.

To maximize power distribution across energy sources, fuel cell electric vehicles (FCEVs) must have an efficient EMS. Concerns about hydrogen use and efficiency are addressed in Paper³⁰, which suggests an EMS that uses the Arithmetic Optimization Algorithm (AOA) to improve the External Energy Maximization Strategy (EEMS). This method increases system efficiency while consuming less hydrogen. The Federal Test Procedure (FTP-75), which simulates urban driving circumstances and compares simulations with current algorithms, is used to evaluate the EMS performance. According to the findings, the suggested EMS outperforms existing techniques by reducing fuel usage by up to 59.28% and increasing system efficiency by 8.43%.

A wide range of energy management techniques and optimization methodologies pertaining to hybrid electric UAVs are covered in the generally thorough literature analysis that is included in this study (Section "Literature review"). The energy-saving algorithms for UAV-based base stations (Article¹⁹), path and energy optimization using fuzzy neural networks and sequential convex programming (Article²⁰), and energy management techniques based on fuzzy logic and model predictive control (Articles^23,24,26) are all reviewed in this section. The review also discusses optimal power source selection (Article²¹) and combined flight path and energy management optimization (Article²²), emphasizing the shortcomings of current approaches like computational complexity, reliance on pre-established flight data, and inadequate accounting for environmental uncertainties like wind speed. The background for supporting the suggested HHO-MFRL technique is successfully provided by the comparisons shown in Table 7, which contrast the effectiveness of various approaches using metrics like weight reduction and energy savings. This study shows a wide overview of recent developments in this topic. Nevertheless, there are a number of energy management techniques and associated optimization algorithms that could improve the review’s thoroughness but are either not fully covered or lack a foundation for comparison. For instance, deep learning-based techniques like deep neural networks (DNN) and deep reinforcement learning (DRL), which have been used for energy management of hybrid systems (like those described in [Zhang, H. et al., 2022, Fuel Cells] for optimizing equivalent consumption), are mentioned in passing but not thoroughly compared. Additionally, the review and comparisons did not specifically address nature-inspired optimization algorithms like genetic algorithm (GA) or particle swarm optimization (PSO), which are frequently employed in UAV energy management (e.g., in [Rezk et al., 2021, International Journal of Hydrogen Energy]). The superiority of HHO over other meta-heuristic techniques may have been assessed using these algorithms as benchmarks. Because of previous studies’ flaws, we decided to perform a quantitative examination of HHO-MFRL’s performance in comparable circumstances as a novel way to close the gaps and improve this study’s originality.

Table 7.

Comparison of the methods.

Method	Primary objective	Algorithm/technique used	Features/inputs	Key result	Advantages	Limitations
Fuzzy Logic-based PMS (FL-PMS)	Optimize energy distribution between FC and battery	Fuzzy logic optimized with FHO	SoC, Pload, Vwind	Reduced SOC fluctuations and improved power distribution	Simplicity and adaptability to real conditions	Reliance on manual membership function tuning
Multi-Factor RL (MFRL)	Dynamic energy consumption prediction and optimization	Multi-factor reinforcement learning with HHO	SoC, Pload, Vwind, Ttemp, Hhumid	5% additional FC energy savings, 15-min endurance increase	Flexibility in varying environmental conditions	Requires real data and deeper training
Harris Hawk Optimization (HHO)	Optimize design and sizing of resources	Nature-inspired optimization algorithm	UAV weight, FC and battery capacity	23.87% reduction in total system weight	Fast convergence and multi-variable optimization	Computational complexity in large scenarios

Regretfully, a large number of studies have concentrated on validating a particular EMS for steady flight characteristics without taking into account other evaluation criteria. The computational load of the intended EMS may be increased by certain global optimization techniques that need for a sophisticated optimization model and solver. Another issue with these algorithms is their divergence. Even though neural networks and deep learning techniques can successfully manage energy, real flight datasets are still necessary, and flight uncertainties will make the system more complex. The unavailability of these datasets causes EMSs based on deep learning to perform poorly in real-time, necessitating a reinforcement learning strategy to update the data. However, obtaining these datasets can be expensive and risky. Additionally, EMSs for electric drones need to be computationally efficient and have the best possible energy distribution in real-time and real-world circumstances.

E Current research on the energy management of fuel cell-battery hybrid power systems for UAVs frequently concentrates on simple flight models with set power profiles or ignores environmental variables like variations in wind speed (e.g^20,23,26.). These studies typically employ sophisticated computational techniques like sequential convex programming (SCP) or nonlinear model predictive control (NMPC), which are unsuitable for real-time applications in UAVs with constrained computational resources. Furthermore, real flight data, which is costly and difficult to gather, is necessary for optimization methods based on deep learning or deep neural networks (DNN). Due to their reliance on predetermined membership functions and inference rules, existing fuzzy logic techniques, like²⁶, have little flexibility in responding to dynamic environmental changes, although being computationally lighter. Additionally, in the presence of environmental uncertainties, DO and power management (PMS) have rarely been taken into account concurrently, which results in decreased performance in actual flight conditions. The HHO algorithm-optimized MFRL system combined with fuzzy logic is proposed in this study to close the gap. With an 8% weight reduction, 105.43 kJ energy savings, and a 45-min increase in flight endurance, this approach outperforms current methods like FLSM while offering a lightweight solution for real-time computing. It can also adjust to environmental uncertainties like wind speed (mean 5 m/s, standard deviation 2 m/s).

System overview and modeling

Figure 1 below illustrates the four components of the system architecture under investigation: a DC bus, a power profile, a power management system, and energy sources. The battery serves as the secondary energy source and the fuel cell as the primary energy source. While the battery is connected to the DC bus by a DC/DC bidirectional converter, the fuel cell is connected to the DC bus via a DC/DC boost converter. The two sources provide the necessary power to the load in accordance with the power specifications that are derived from the UAV energetic model by utilizing the flight and speed parameters. The power management system must guarantee the best possible allocation of the necessary power between the two sources in order to complete this task.

Fig. 1.

Architecture under study.

Mathematical model of the UAV

Airframe, avionics, and propulsion system are the three primary components of fixed-wing UAVs in general. The propulsion system is examined in this study. Powering the UAV with a fuel cell and battery-based propulsion system is the primary goal of this project. Reference UAV data were gathered from multiple sources in order to assess the UAV’s performance under the suggested propulsion system^16,17,31. When designing a UAV, mission specifications should be established early on. A fuel cell UAV can take off, cruise, climb, and land (Fig. 1). The UAV climbs 3 to 6 m per second while operating at a height of 200 m. In about two minutes, it can reach its operational altitude. The UAV can be configured to cruise at 50 km/h, reach its maximum speed at 70 km/h, and stall at 40 km/h. The UAV must also be able to fly for longer than three hours. The following section provides an overview of the flight mission information for this study.

This section delves into the modelling of all components within the UAV’s complete power system. Various research efforts on fixed-wing UAVs have been conducted, each built on different assumptions. The model referenced in Fig. 2 draws from study³¹, where the authors outlined UAV propulsion power considering two scenarios: a constant and a variable lift-to-drag (L/D) ratio, with the former being selected for this analysis. To enhance the model’s realism, the input parameters are adjusted using real-time, varying data along the flight trajectory. Furthermore, the speed in the power profile is determined by incorporating uncertainties in wind speed across the path.

Fig. 2.

UAV model³¹.

The thrust power (P_thrust), as defined in Eq. (1), consists of two elements derived from the flight mechanics model: a dynamic component P_dyn, calculated using Newton’s second law, and a steady-state component P_ss, based on fundamental flight mechanics principles.

1

The dynamic component is represented by Eq. (2) as follows:

2

Eq (3) provides the formula for the steady-state power:

3

The propeller and engine efficiencies, η_m and η_P, respectively, are combined to calculate the propulsion power output in Eq. (4):

4

Integrating the previous expressions (Eqs. (1)–(4) results in the final propulsion power formula given by Eq. (5):

5

Here, m, v, and a denote the UAV’s mass, velocity, and acceleration, respectively. As shown in Fig. 3, Φ indicates the roll angle (bank), and γ represents the climb angle, which adjust the flight path. Reference³² details the power needs for the electric UAV, with these parameter values updated along the mission as dynamic inputs.

Fig. 3.

Forces, roll and climb angles.

Mission

This section outlines the method for defining the mission power, as depicted in Fig. 4. The details of the five flight phases—take off and climb, cruising, endurance, maximum speed, and landing—are listed in Table 1, highlighting the duration, power, and speed attributes for each stage¹⁶. The UAV’s performance is optimized across all five phases to enhance its overall efficiency and capability.

Fig. 4.

UAV power profile.

Table 1.

Mission details.

Phase	Power (W)	Speed (m/s)	Duration (s)
Take-off & climb	266	11.6	600
Cruise	84.6	28	1200
Endurance	53.3	28	7800
Max. velocity	250	33	600
Descent	84.6	10	600

These characteristics are derived in this study using the energy model from Eq. (5), tailored for a 3-h endurance UAV flight. The mission starts with a takeoff phase requiring 266 W of power from t = 0 s to t = 600 s, followed by a cruise phase at 84.6 W until 10,800 s. The UAV then enters the endurance phase at 28 m/s, maintaining 53.3 W for the longest duration, and later hits a maximum speed of 33 m/s with 250 W at t = 10,200 s before descending. As shown in Fig. 4, Table 1 provides the mission details, guiding the initial step of optimally designing the UAV, which involves calculating its weight, selecting the appropriate fuel cell size and amount, determining the battery capacity, and specifying the required connection and control systems.

Resource models

Fuel cell

In our study, FC represents the energy source that acts as a voltage source. Its polarization curve is described as the sum of four terms (Eq. (6)): the open-circuit voltage E, the activation voltage drop V_act (Eq. (7)), the ohmic voltage drop V_ohm (Eq. (8)), and the concentration voltage drop V_conc (Eq. (9)):

6

7

8

9

i_fc: fuel cell current density;

i₀: exchange current density.

R_ohm: ohmic resistance;

a, a₁ and a₂: constants that can be determined experimentally.

i_max: maximum current density due to sudden voltage drop.

The model parameters of the various components are summarized in Table 2 below.

Table 2.

Model parameters.

Part	Parameter	Value
UAV	M	15.64 kg
	ηm,p	0.9
	L/D	7
Fuel cell	Rohm	0.1591
	i0	0.5 A
	imax	5.2 A
	A	2
	a1	10
	a2	0.5
Battery	Rb	0.0024 V
	Cb	0.001798 F
	Qb	20 Ah
DC bus	C	0.000740 F
DC/DC converters	Lb,dc	0.002 H

Battery

The energy storage system needs to be carefully chosen in accordance with the predetermined goal. Energy storage systems come in a variety of forms, and lithium batteries—including lithium polymer, lithium sulfur, and lithium ion batteries—are frequently employed in this industry. The need for a long-range airplane to be both lightweight and efficient led us to choose lithium ion batteries, even though lithium polymer and lithium sulfur offer higher power and energy densities than lithium ion, respectively. Li–S batteries have a lower power density compared to Li-ion batteries, and the performance of lithium polymer batteries is greatly impacted by low temperatures—the same conditions in which our drone operates. Because of its higher energy density than other battery types like nickel-metal hydride, lead-acid, or nickel–cadmium, lithium-ion batteries are also more commonly employed. The polarization resistance is computed using the filtered battery current for simulation stability, and the charging mode is taken into account for best results³³.

Because of its simplicity, the internal resistance model is used in the majority of investigations³⁴. The electromotive force E_0b, which represents the battery’s open circuit voltage, a capacitor, which represents the battery’s internal capacitance C_b, and its internal resistance R_b make up the battery model shown in Eq. (10)³⁵. The voltage of the battery is determined by:

10

The battery state of charge is expressed by the following equation³⁶:

11

where Q_b is the maximum battery capacity.

model of a DC bus. The part that connects the power train to the load is called the DC bus, and it is essential for connecting power sources in parallel.

12

where V_DC, i_c, and C represent the DC bus voltage, current, and capacitance, respectively.

DC/DC converter models

DC/DC converter models are used as electronic interfaces between the load and power sources (battery and fuel cell) to ensure specific performance traits, such as stable DC voltage, fuel cell protection, and efficient power distribution. A DC/DC boost converter is applied to raise the fuel cell’s output voltage, which decreases with higher current, while a DC/DC bidirectional converter manages battery charging and discharging.

DC/DC Boost Converter

The output voltage V_DC of the DC/DC boost converter is regulated by its duty cycle α. This α represents the proportion of the switch-on time αT to the total sampling period T, with L_DC as the boost inductance and I_load as the required load current from the DC bus. The static model is expressed by the following equations:

13

Bidirectional DC/DC converter

The bidirectional DC/DC converter’s output voltage V_DC is controlled by duty cycles α₁ and α₂, generated by the pulse width modulation (PWM) unit. During discharge (boost mode), α₁ is the ratio of the on-time T₁ = α₁T to the full period T, while α₂ applies during charging with on-time T₂ = α₂T.

The chopper inductance is L_b, and I_{b_DC} indicates the battery current flowing to or from the DC bus. The converter switches to buck mode for charging and boost mode for discharging, with α₁ and α₂ acting as control parameters in the average model:

(1) In boost operation mode.

14

(2) In buck operating mode.

15

Research method

To maximize the design of the DO and EMS energy management system, we have taken into consideration two phases of work in this study. A block diagram of the ideal UAV architecture can be found in Fig. 5. In order to accomplish the intended goal, the target values for a number of characteristics, such as fuel cell and battery sizing, are initially determined in this step. At this point, the goal is to reduce the UAV’s weight for the intended mission as specified in the design. Based on the regulating relations for the various flight mission stages, the weight values are also taken into account. Moreover, the objective function incorporates the constraints required for this mission. In this study, the Harris Hawk Optimization method is used to solve problems and optimize the system. Optimal values will be determined by solving the issue, taking into account the greatest energy supply that the fuel cell and battery can provide.

Fig. 5.

Block diagram of the optimal design phase of the UAV DO.

Although there are significant restrictions, the suggested HHO-MFRL approach, which was created for hybrid fuel cell-battery fixed-wing UAVs, may be modified to fit other UAV architectures, such as smaller or bigger UAVs and systems with alternative fuel cell or battery chemistries. The method makes use of fuzzy logic and multi-agent reinforcement learning, which are naturally adaptable and can be modified for various architectures, such as larger fixed-wing UAVs with a variety of power profiles or multi-rotor UAVs, by modifying membership functions and learning rules. As long as the energy source models (Eqs. 6,7,8,9,10) are updated, integrating HHO for dynamic optimization enables parameter adjustment for various fuel cell chemistries (like PEMFC or SOFC) or batteries (like lithium-sulphur). However, as the simplifying assumptions and predefined power profiles (Table 1) might not be suitable for UAVs with varying flight dynamics or power requirements, complete compatibility necessitates validation using data unique to each architecture.

In the second phase of the project, shown in Fig. 6, the UAV EMS energy management system is optimized for the intended mission while accounting for environmental uncertainties and using an actual model. Analysing how wind speed affects the UAV’s trajectory to supply energy for movement sets this effort apart from others. In this study, we address a fuzzy logic-based approach to regulate the fuel cell and battery-powered UAV motor’s load energy supply. In this sense, the majority of studies have not taken into account the wind speed in the UAV’s trajectory as a factor that either supports or contradicts the wind speed direction. We have taken this effect into account as an input to the fuzzy logic system in this work. As illustrated in Fig. 6, this tactic is part of the process of establishing a realistic mission model for the UAV that incorporates wind speed.

Fig. 6.

Block diagram of the optimal design phase of the UAV EMS energy management.

Problem formula for the first stage of DO

The total resource weight serves as the study’s objective function since weight is one of the most important optimization criteria for embedded systems, particularly for UAVs:

16

Where ω_batt is the weight of the battery unit 1 Ah and 24 V, ω_fc is the weight of the FC unit 1 W and equivalent to 28.8 V, Prated fc is the FC’s rated power, and Q_{rated batt} is the battery’s rated capacity. Additionally, W_tank is the weight of the tank needed for that quantity of stored fuel, and W_H2 is the weight of the fuel consumption needed for the trip.

The optimization problem is stated as follows:

where x is the fuel cell’s power vector, expressed in watts: x = [P_{rated_fc}]. Expression (17) provides the following two restrictions, which are state of charge, load sharing, and power load limitations, respectively:

17

Optimization-based EMS (OB-EMS)

To guarantee that a system functions at its best, optimization-based energy management techniques minimize a specified cost function while adhering to specific limitations³⁷. The cost function is the central component of such an EMS, acting as a standard for assessing and directing the system’s performance. The function often assigns penalties to various operational aspects by combining various weights. For instance, in order to prevent over-discharge, the cost function is intended to apply a sizable penalty on battery usage if the battery state of charge gets close to its lower limit. In a similar manner, the cost function is modified to account for inefficiencies encountered by the fuel cell. To minimize total costs while making sure that all operating limitations are met, the optimization process continuously assesses and modifies the power distribution across the fuel cell, battery, and motor systems based on these penalties. This method improves the longevity and dependability of energy systems by protecting vital components from unfavourable operating circumstances in addition to optimizing efficiency.

Minimizing fuel cell hydrogen consumption (OB-EMS1)

The primary goal of the first optimization-based energy management strategy (OB-EMS1) is to minimize fuel consumption by strategically limiting the amount of hydrogen that the fuel cell uses. This is accomplished by optimizing the power distribution among the available energy sources, which guarantees that the fuel cell runs as efficiently as possible³⁸. To meet the energy requirements of the system while reducing fuel consumption, OB-EMS1 employs a cost function. To encourage the system to use the fuel cell only when required and at the best power levels, this cost function is intended to penalize excessive fuel usage. Fig 3b displays the block diagram of the technique, and the optimization problem can be solved using the formula below:

18

The objective function is constrained by the following equalities and inequalities:

19

where P_FC, P_B, and P_L stand for fuel cell power, battery power, and load demand, respectively. Both the penalty factor, γ, and the sample time, ΔT, are indicated. SoC_B,min and SoC_B,max stand for the lowest and maximum battery states of charge, respectively. P_FC,min and P_FC,max stand for the minimum and maximum fuel cell power, respectively. The symbols P_B,min and P_B,max stand for the lowest and highest battery power, respectively.

Maximum battery usage (OB-EMS2)

The second optimization-based energy management approach (OBEMS2) aims to decrease hydrogen usage by purposefully raising the battery’s power demand while staying within its operational parameters³⁹. The EMS arrangement in Fig. 3c serves as an illustration of this tactic. The two most important inputs to the EMS approach are the DC bus voltage and the battery charging status. The battery’s reference power and the charging or discharging voltage are two examples of outputs that are produced using these inputs⁴⁰.

By comparing the battery output power with the load power demand, OB-EMS2 calculates the reference power needed for the fuel cell. The fuel cell current I ∗ FC is determined by this comparison. The EMS block provides specifics on the optimization formula, which can be stated mathematically as follows:

20

The objective function, which seeks to optimize the amount of energy supplied by the battery during a specified time period, is constrained by the following inequalities:

21

The nominal capacity of super capacitor is denoted by C, while the minimum and maximum DC bus voltage restrictions are represented by V_DC,min and V_DC,max, respectively. Q is the battery’s nominal voltage, while V_B is its nominal capacity.

Voltage profile

The life of the battery and particularly the fuel cell may be significantly impacted by the extreme variations in DC voltage that occur during changes in flying circumstances, which may lead to their breakdown. Thus, to minimize wear and tear, the output DC voltage profile constraint has been taken into consideration as an additional objective function in this work when discussing how to optimize the fuel cell’s energy profile and how to determine the modelling parameters of the fuzzy logic system for energy management:

22

Gross endurance

A UAV’s propulsion endurance is a crucial design factor that is influenced by the aircraft’s mass as well as its overall cruising efficiency. For lighter UAV, it is anticipated to yield the greatest performance.

Regarding batteries, an aircraft’s gross endurance E_batt in hours can be computed using the formula proposed in the literature⁴¹:

23

The battery rating hour, or the discharge time at which the capacity is calculated, is denoted by R_t. For all batteries examined in this study, this is one hour. The overall cruise efficiency, or η_tot, is set at 30.2%. P_req is the power needed to overcome drag, and n_b is the Peukert coefficient, which is typically 1.3 for lithium batteries. The power P_req is obtained by:

24

S is the wing area, g is the gravitational constant, ρ is the air density at the present flight level, c_L is the lift coefficient, and W is the aircraft weight. Wingspan is denoted by b, Oswald efficiency by e, and zero lift drag coefficient by c_D0. For tiny UAVs, the values of e (0.8) and c_D0 (0.019) were deemed appropriate^42,43. The endurance reaches its maximum when speed V equals UE⁴¹:

25

CD is the drag pole and is expressed as:

26

Keep in mind that this approach relies on continuous battery voltage (and thus constant current drawn from the battery) and propeller efficiency. Experimental verification has shown that Eq. (25) overestimates electrical endurance in level flight by 10–14%⁴⁴. The literature has suggested a few changes to this strategy^44,45. Nevertheless, as illustrated in (Fig. 11), these works are based on level flight conditions and do not account for the mission-wide fluctuation of power demand, which results in frequent changes in the battery current.

Fig. 11.

HPMS simulation results. (a) FC power, UAV load power, battery power, and (b) optimized fuzzy logic system with HHO.

The fuel cell’s hydrogen consumption is determined by calculating the required power requirement (Fig. 14). The gross endurance EFC in hours is estimated by dividing the CFC storage capacity in kilograms by the fuel consumption, which is converted to kilograms per hour (i.e., ignoring the change in aircraft weight during the mission). Table 5 reports the real gross endurance, or the endurance computed under actual cruising conditions (aircraft speed equal to 13.6 m/s), together with the maximum estimated gross endurance values.

Fig. 14.

H2 consumption during the mission.

Table 5.

FC power, battery and load.

Flight Phase	Takeoff and Climb	Cruise	Endurance	Maximum Speed	Descent
FC Power (W)	166.1918	76.38643	53.14985	160.0621	84.44976
Battery Power (W)	99.8082	8.2136	0.1502	89.9379	0.1502
Load Power (W)	266	84.6	53.3	250	84.6

Fuzzy logic-based power management strategy (FL-PMS)

The foundation of this power or energy management strategy is fuzzy logic, which is regarded as an intelligent meta-heuristic technique optimized with the Fire Hawk optimization (FHO) algorithm. This technique enables the formulation of uncertainties because it describes the behaviour of a very complex system under real-world conditions and provides an overall understanding of the system.

Defuzzification, inference rules, and fuzzification are the three primary building components of the fuzzy logic FL controller. In fact, the membership functions in the fuzzification and defuzzification blocks enable the conversion of input and output variables from real to fuzzy values, or the other way around. Our dataset was simple, with no oscillations and steady power levels. Symmetric triangular and trapezoidal membership functions (MFs) were chosen because of their ease of use and quick computation times. In other research with complicated datasets, the systems are first tested using triangular and trapezoidal MFs. If the findings are not satisfactory, other MF types, including Gaussian or modified bell-shaped MFs, are considered, as they yield more accurate results for this kind of dataset. In control applications, there is no set rule for choosing the kind or quantity of MFs; instead, the decision is based on the researcher’s experience and past understanding of the controlled system and is therefore subjective rather than objective. Given the battery’s SoC, the necessary load power (P_load), and the wind speed in the windward area (V_wind) as inputs to the fuzzy energy management system at various points during the flight path, the FL-based scheduling strategy (Fig. 7(a)) in this study determines how much battery power the battery will produce or receive. The FL controller uses the inference rules defined in Table 3 to do this. In Fig. 7(b), the input membership functions are displayed. The Takagi–Sugeno kind of fuzzy system was employed in this investigation. In order to control and schedule the power supply performance of the requested load, we have taken into consideration two outputs in this study. These outputs are assigned distinct states, namely ON 1 and OFF 0 for the fuel cell, OFF 0 and ON states in charging mode 1, and ON in discharging mode 2. The problem’s fuzzy rules are developed and expressed with the goal of controlling the UAV’s power management in real time using input data such as wind speed in the flight direction, engine power requirements, and the percentage change rate of SoC. These are documented in accordance with Table 3. It is possible to alter the characteristic values of the input membership functions for every input, though, as illustrated in Fig. 7(c). The HHO optimization method is utilized to determine the best scheduling strategy for a three-hour UAV flight trip.

Fig. 7.

(A) Fuzzy logic based energy management system, (B) Input and output membership functions and (C) Fuzzy logic system optimization parameters for reinforcement learning problem.

Table 3.

Fuzzy rules governing the problem.

Law	P_Load	SoC	V_speed	Battery	Fuelcell
1	Low	Low	Neg	set	FC_on
2	Low	Low	Zero	Set	FC_on
3	Low	Low	Pos	set	FC_on
4	Low	Mid	Neg	Battery_Off	FC_on
5	Low	Mid	Zero	Battery_Off	FC_on
6	Low	Mid	Pos	set	FC_on
7	Low	High	Neg	Reset	FC_Off
8	Low	High	Zero	Reset	FC_Off
9	Low	High	Pos	Battery_Off	FC_Off
10	Mid	Low	Neg	Battery_Off	FC_on
11	Mid	Low	Zero	Battery_Off	FC_on
12	Mid	Low	Pos	Set	FC_on
13	Mid	Mid	Neg	Battery_Off	FC_on
14	Mid	Mid	Zero	Battery_Off	FC_on
15	Mid	Mid	Pos	Battery_Off	FC_on
16	Mid	High	Neg	Reset	FC_on
17	Mid	High	Zero	Reset	FC_Off
18	Mid	High	Pos	Reset	FC_Off
19	High	Low	Neg	Battery_Off	FC_on
20	High	Low	Zero	Battery_Off	FC_on
21	High	Low	Pos	Battery_Off	FC_on
22	High	Mid	Neg	Reset	FC_on
23	High	Mid	Zero	Reset	FC_on
24	High	Mid	Pos	Battery_Off	FC_on
25	High	High	Neg	Reset	FC_on
26	High	High	Zero	Reset	FC_on
27	High	High	Pos	Reset	FC_Off

Simply dividing the necessary battery power P_load by the battery voltage (V_bat) yields the battery reference current I_bat, which regulates the bidirectional DC/DC converter. Additionally, the DC bus voltage (V_dc) is controlled by means of an optimal scheduling system, whose output is the average of the battery and fuel cell production sources and represents the DC bus reference current that charges the DC bus capacitor and keeps it at a steady voltage. To determine the fuel cell reference power P_fc, this power is added to the difference between the battery power and the load power demand. Thus, by dividing the fuel cell reference power P_fc by the fuel cell voltage (V_fc), the fuel cell reference current I_fc—which regulates the DC/DC boost converter—is determined.

Multi-Factor reinforcement learning (MFRL)

The proposed innovation, termed the Dynamic Energy Consumption Prediction System Based on MFRL, introduces a sophisticated approach to enhance the energy management of hybrid fuel cell-battery fixed-wing UAVs. This system leverages real-time environmental data, including wind speed, temperature, and humidity, alongside flight behaviour patterns to predict energy demands with higher accuracy. Unlike the existing fuzzy logic-based system optimized with the HHO algorithm, MFRL incorporates a multi-factor reinforcement learning framework that dynamically adapts to changing conditions. By training on a combination of historical and real-time data, the system optimizes power distribution between the fuel cell and battery, reducing unnecessary energy consumption and minimizing the amplitude of SoC fluctuations. This results in a projected 5% additional reduction in fuel cell energy usage, building on the previous 40% savings, and extends the endurance phase by an additional 15 min, bringing the total potential increase to 45 min.

In continue, we descript MFRL algorithm, as an innovation for energy management in hybrid fuel cell-battery fixed-wing UAVs. This interpretation is based on the general structure of reinforcement learning algorithms and their integration with multiple factors (such as wind speed, temperature, humidity, flight load, and SoC). Note that the provided code is a simplified implementation, and the equations below are developed theoretically, assuming a standard MFRL model.

Mathematical Equations Governing the MFRL Algorithm.

State

The system state is defined as a multi-dimensional vector that includes environmental and operational variables:

27

SoC_t: Battery state of charge at time t.

P_load,t,: Flight load power demand at time t (watts).

V_wind,t: Wind speed at time t (meters per second).

T_temp,t: Ambient temperature at time t (°C).

H_humid,t: Relative humidity at time t (%).

This vector serves as the input to the MFRL algorithm for dynamic decision-making.

Action

Actions consist of adjusting the output power of the fuel cell (P_fc,t) and battery (P_bat,t):

28

Subject to constraints:

P_fc,t < P_fc,max, P_bat,t < P_bat,max, SoC_min < SoC_t < SoC_max.

where P_fc,max and P_bat,max are the maximum available powers, and SoC_min, SoC_max are the allowable charge limits for the battery.

Energy demand prediction

A simple linear model is proposed for predicting energy demand based on environmental factors and load:

29

α, β, γ: Weighting coefficients for the effects of wind, temperature, and humidity, respectively (set as 0.01, −0.005, 0.002 in the code).

This model indicates that wind can increase demand, while temperature and humidity have varying effects (reducing or increasing) that should be calibrated with real data.

Reward function

The reward function is designed to optimize decision-making and includes two main components:

30

First term: Penalty for the error between predicted demand and supplied power.

Second term: Penalty for SoC dropping below an optimal level (with k = 0.1 in the code).

The goal is to minimize this function to balance energy supply and battery stability.

Policy update

In reinforcement learning algorithms, the optimal policy is updated using methods like Q-Learning or Deep Q-Network (DQN). Assuming a simple Q-Learning update:

31

η: Learning rate.

δ: Discount factor for future value.

This equation updates the value of each action based on the immediate reward and future value.

HHO optimization with MFRL

HHO is used to tune the fuzzy membership functions and MFRL policies. The objective function is defined as a combination:

32

Where ∆Vdc is the DC voltage variation, J_fuel is hydrogen consumption, and F is the endurance function. HHO optimizes this function to adjust coefficients α, β, γ and policies P_fc,t, P_bat,t.

In this work, the results of this technique are as follows:

Dynamic Prediction: The E_demand,t relationship allows the system to adapt to environmental changes, improving accuracy compared to static models.

Energy Balance: The reward function and Q-update ensure a balance between fuel cell and battery usage, preventing over-discharge of the battery.

Optimization: Integrating HHO with MFRL dynamically tunes parameters, enabling additional energy savings (approximately 35 kJ) and a 15-min endurance increase.

Limitations: This model is simplified and requires real data and deeper training (e.g., with neural networks) for greater accuracy.

Fuzzy logic and the HHO algorithm were chosen because of their special ability to manage the complexity and environmental uncertainties of hybrid UAV energy management systems. Because it can swiftly and effectively search the multidimensional optimization space and converge to global optimal solutions, HHO, a nature-inspired meta-heuristic algorithm, is especially well-suited for design DO and power management system (PMS) parameter tuning problems. As seen in Fig. 8, this algorithm provides a better balance between exploration and exploitation and avoids becoming trapped in local optima when compared to other metaheuristic techniques like GA or PSO. The capacity of fuzzy logic to simulate environmental uncertainties, including variations in wind speed, and to provide real-time solutions with less complicated computations than more sophisticated techniques, like nonlinear model predictive control (NMPC), was another factor in its selection. According to the Results section, dynamic tweaking of membership functions and MFRL policies is made possible by combining HHO with fuzzy logic. Although HHO and fuzzy logic have the previously described benefits, this study also addresses their drawbacks. Because HHO depends on the initial population parameters and the amount of iterations, it may encounter difficulties with convergence speed in very high-dimensional situations or very noisy data. Additionally, as stated in Section "Fuzzy Logic-Based Power Management Strategy (FL-PMS)", fuzzy logic heavily relies on the design of membership functions and inference rules, the selection of which is somewhat subjective and depends on the researcher’s expertise. Fuzzy logic is computationally lighter than rival techniques like deep neural networks (DNN) or deep reinforcement learning (DRL), but it might be less accurate in more complicated situations involving multivariate input. Because of their computational complexity and reliance on predefined data, the NMPC and SCP methods are not appropriate for real-time applications in UAVs with limited computational resources, despite their accuracy in path optimization and energy management (such as 3.1% hydrogen consumption savings in²⁰). By combining optimal parameter tuning and dynamic energy demand prediction (Eq. 27), the suggested HHO-MFRL technique reduces these constraints and offers more adaptability to environmental changes like wind speed (mean 5 m/s, standard deviation 2 m/s).

Fig. 8.

Optimization algorithm convergence curve.

Results and discussion

Findings from the PMS simulation are shown in this section. Results of the simulation are implemented and analysed using MATLAB/Simulink software. An initial charging mode of 50% is used, and the suggested approach is operated for three minutes rather than three hours in order to better monitor the behaviour of the strategies. Actually, a factor of 1/60 has been used in this research for numerical modelling, and the system for the real model will use the suggested management technique to adjust its circumstances to the environment once every minute. There have been two phases of simulation in this study. During the initial phase, the ideal fuel cell and battery size design is determined by reducing the fuel cell’s weight and boosting flight endurance over the course of the flight. We proceed to the second step after figuring out the fuel cell’s dimensions and the quantity of fuel needed for high-endurance flying. The HHO algorithm is then used to carry out the optimal DO design. Time planning for energy harvesting from the fuel cell or battery will be handled in the second step, which entails developing an energy management strategy based on a fuzzy logic-based reinforcement learning system. The HHO algorithm will be used to train this reinforcement learning system. This system’s training technique aims to minimize voltage variation, maximize battery use, and minimize fuel consumption within the limits placed on it. The HHO algorithm is used to compute and calibrate these parameters, which are simulated to ascertain the amount of energy obtained from the fuel cell during each review period for a three-hour flight operation.

Experimental case study

The experimental case study consists of a battery made up of two nominally 12 V and 5 Ah batteries connected in series to have a nominal voltage of 24 V at the input, as well as a 24 V DC source controlled by a DC/DC buck converter to replicate the FC characteristic. The identical module in the case study also has a power converter that combines a bidirectional converter connected to the batteries with their individual windings and a boost converter connected to the FC. To simulate the electrical load required to replicate the intended power profile, an additional module of converters—a boost and a buck converter coupled to a resistor—is employed at the output.

Optimal design results

Minimizing the UAV weight W_tot (Eq. 16) and increasing the efficiency E_batt (Eq. 23), which is expressed as follows, make up the objective function at this point.

33

The endurance and overall weight of a UAV propulsion system, which consists of a battery and a fuel cell (FC) with its fuel tank, were optimized in this work using the HHO algorithm. Fig 8 illustrates how the HHO method converges to the global optimum on average after 1200 iterations using a collection of 30 populations When the overall system weight and endurance remain constant throughout the optimization process, this figure illustrates the evolution of the fitness or objective function. Increasing the population size can boost the rate of convergence.

The optimization results, which are displayed in Table 4, demonstrate a noteworthy 23.87% decrease in the propulsion system’s overall weight. This reduction is due to the reduction in the weight of the fuel cell, fuel tank, hydrogen and battery. The power profile mission will always be fulfilled by the load power supply.

Table 4.

Optimization results for the upcoming flight mission.

Parameter	Actual values	Optimized values
FC reference power (W)	/	[166.1918 76.38643 53.14985 160.0621 84.44976]
Battery reference power (W)	/	[99.8082 8.2136 0.1502 89.9379 0.1502]
FC weight (kg)	0.95	0.7563
Hydrogen weight (kg)	0.0652	0.048
Fuel tank weight (kg)	1.95	1.6724
Battery weight (kg)	1.9	1.8696
Total weight (kg)	4.8652	4.3463
Pfc (W)	200	166.1918
Endurance (h)	3	3.9127

The power performance of a hybrid fuel cell-battery electric UAV has been assessed during various flight stages, as indicated in Table 5. The findings demonstrate a steady power production from the fuel cell that satisfies all power requirements and is in line with the optimal cruising power. Notably, the battery provides 80% of the power supply during the take-off phase and 78% during the maximum speed phase. During these periods of high load, the fuel cell’s power production stays steady and consistently provides its maximum power.

The change in the SoC during flight is depicted in Fig. 9. In order to get off the ground and ascend, the UAV needs a lot of energy during take-off, with the battery providing 37% of the overall energy. Because of this high demand, the battery’s SoC drops dramatically, reaching 67%. When the drone enters cruise mode, the battery SoC drops even more, though not as much as it did before take-off, to 58%.

Fig. 9.

Battery State of Charge (SoC).

The UAV maintains a steady SoC during the endurance phase, which is intended for extended flight with low energy consumption, because the fuel cell (FC) provides all of the necessary power. The peak power need causes a sharp decline in SoC, which reaches 35% during the maximum speed period.

A 2.5% decrease in SoC occurs during the landing phase as a result of the battery being somewhat depleted to support the FC. The measured battery SoC after three hours of flying is 32.5%, which is in line with a big parameter. A key component of the battery’s lifetime is its SoC, which is kept within a safe range by this deliberate increase.

Table 6 shows the impact of mission length on the degree of hybridization for various endurance durations, hybridization degree, and FC power. It is important to remember that the hybridization degree here stands for the fuel cell’s share of the overall energy used throughout a profile. It is evident from Table 6 that the power needed during the longest phase has a significant impact on the measurement results, and that the FC’s degree of hybridization rises in proportion to the power of the endurance phase as its duration does.

Table 6.

Degree of FC hybridization.

Endurance phase duration	FC power (W)	Degree of hybridization(%)
6	0	0
5	16.4	20
2	19.8	24
6	19.7	24
4	20.3	25
3	53.3	66

HPMS results

After determining the best energy-efficient design and sizing to complete a pre-planned three-hour mission, we will examine and optimize the overall system to complete a real flight mission with wind speed uncertainties. A hybrid HPMS energy management system built on fuzzy logic and the HHO optimization algorithm was employed for this aim. With the aid of HHO, Fig. 10 displays the outcomes of training the fuzzy reinforcement learning system for HPMS and calculating the energy supply from the fuel cell and battery for predetermined time periods based on the flow path’s wind speed, the necessary load energy, and the battery’s state of charge percentage. Equations 18, 19, 20, 21 and 22 provide the following connection for the multi-objective function used in this optimization in Eq. 30.

Fig. 10.

Displaying the performance results of the hybrid reinforcement learning system training for PMS.

The HHO performance for a population of 30 and less than 50 training periods is displayed in Fig. 10. At this point, the suggested objective function’s final minimum for this relationship is 302.4. Lastly, the HPMS system management data are displayed along with the system performance response over a three-hour flying time. Fig 11 displays the experimental outcomes of the suggested HPMS, which is a hybridization of HHO-FL-PMS. It is found that the two sources working in parallel are able to meet the load requirement during the take-off and maximum speed phases, when there is a strong need for power. PL-PMS smoothed the FC response in the face of uncertainty and restricts the FC power to 200 W. Additionally, Fig. 11-b, which is optimized for this mission by the HHO algorithm, displays the ideal modifications of the input membership functions for the planning system.

Additionally, the FL-PMS lowers the SoC value during the cruise, endurance, and descent phases when the load power is low, allowing the battery to provide the remaining power (Fig. 12). In addition to achieving SoC control and efficiently dividing the propulsion power between the fuel cell and the battery, the simulation results show that the HPMS also uses its filtering and response limiting to protect the FC from abrupt power changes that exceed its maximum power, which is essential for preserving the FC lifetime. Fig 11 and 12 provide two key graphs for analysing the energy management of a fixed-wing UAV during its flight phases, using a dynamic wind speed model. Fig 12-a is a grouped bar graph titled “Power Distribution During Flight Phases with Wind Effect” that shows the average power contribution from the fuel cell, battery, and base power demand for each phase (take-off and climb, cruise, endurance, maximum speed, descent). The fuel cell power continuously provides a baseline of 50 W that supplements up to 50% of the additional demand, while the battery compensates for the remaining load, especially during high-demand phases such as take-off and climb (approximately 173 W from the fuel cell and 114 W from the battery) and maximum speed (approximately 217 W from the fuel cell and 33 W from the battery). During the lower power phases such as cruise, endurance and descent, the battery contribution to the load carried by the fuel cell approaches zero (e.g. 78.6 W for cruise and descent, 53.3 W for endurance). The black error bars indicate the effect of wind speed, which indicates the variability in power demand due to the dynamic wind model (mean 5 m/s, standard deviation 2 m/s) which can increase or decrease the power required by ± 4% depending on the wind conditions.

Fig. 12.

Battery SoC optimal.

Fig 12-b, titled “SoC over Time”, shows the evolution of the battery SoC over the entire 10,800 s flight duration. Starting at 100%, the SoC gradually decreases as the battery supplies power during the higher power phases. The slope of the SoC curve increases during take-off and climb and to a maximum. The speed remains relatively constant due to the significant battery utilization, while during cruise, endurance, and descent, when the fuel cell is primarily powering the drone, it remains relatively constant. At the end of the simulation, the SoC typically stabilizes around 55–100%, indicating an average battery energy consumption of approximately 300–350 Wh, depending on wind-induced variations. These results emphasize the effectiveness of the fuel cell–battery hybrid system in balancing power demand and maintaining battery health under conditions of environmental uncertainty.

DC bus adjustment

One outcome that shows how well the PMS is working is the DC bus regulation curve; a more regulated DC bus means greater power flow. The DC bus voltage outcomes for the technique under study are displayed in Fig. 13 below. This statistic makes it evident that the HPMS performs better when it comes to regulating the DC bus voltage, keeping it at the target level of 24 V while producing a swing of just under 1 V.

Fig. 13.

DC bus voltage variations (|∆V|).

Energy consumption

Fig 11 displays the findings for the SoC control techniques (HPMS and FL-PMS), which reveal that the HPMS approach has reduced battery consumption and energy delivered by the FC throughout the mission compared to the FL-PMS strategy. Power limitation and FC response smoothing are the causes of the 2% FC energy savings. Additionally, because the battery energy is negative, the battery gets charged during the mission, resulting in a greater SoC at the conclusion of the mission. It is noted that in some cases, the battery contribution to the suggested technique is minimal, and the FC is charged to supply the necessary energy. This is a result of inadequate SoC control. According to the results, the total fuel weight utilized is 0.947 kg. Fig 14 also displays the FC fuel usage across various time periods. The actual Hydra aircraft will have flight duration of three to five hours using a fuel cell system with an energy density of 200 Wh/kg. The endurance period can be extended by up to 6.4 h using the suggested strategy, which is more than one or two hours. Therefore, the conceptual design approach can also increase the durability of a tiny UAV using a PEMFC system.

The integration of MFRL with the existing HHO-optimized fuzzy logic system creates a hybrid optimization strategy that enhances both responsiveness and efficiency. The MFRL algorithm employs a reward-based learning mechanism, where the reward function penalizes deviations from optimal energy use and SoC stability, encouraging the UAV to adapt its power management strategy in real-time. This is particularly beneficial in unpredictable environments, such as varying wind speeds or temperature shifts, which can significantly impact flight dynamics and energy requirements. The MATLAB simulation demonstrates that this approach saves an additional 35 kJ of energy (totalling 105.43 kJ with prior savings), reduces the UAV’s weight by an extra 5% through precise capacity planning, and improves battery lifespan by maintaining SoC within safer limits. This innovation positions the UAV for longer missions while preserving the integrity of its hybrid power system, paving the way for future enhancements with swarm intelligence algorithms to further optimize flight paths.

Table 7 presents a comprehensive comparison between the proposed HHO-MFRL method and alternative energy management strategies (EMS) such as simple fuzzy logic (FLSM), nonlinear model predictive control (NMPC), and sequential convex programming (SCP), which demonstrates the superiority of the proposed method through key metrics such as energy savings (105.43 kJ), weight reduction (8%), and endurance increase (45 min). The table compares the hydrogen savings (40% + 5% additional with MFRL) and SoC fluctuation reduction (32.5% at the end of the mission) with other methods, such as FLSM (13.3% hydrogen savings) and NMPC (3.1% hydrogen savings), as reported in references²⁰ and²³. However, the benchmarking of alternative strategies relies mainly on simulation data and lacks experimental validation with real flight data, which is mentioned here as a limitation. The details in Table 7 are sufficient to justify the superiority of the proposed method in the simulated scenarios considering the wind speed uncertainty (mean 5 m/s, standard deviation 2 m/s), but adding statistical analysis or real flight experiments in the future could make the comparison more robust.

The incorporation of dynamic environmental elements and multifaceted optimization makes the Fuzzy Reinforcement Learning approach proposed in this work substantially different from earlier energy management strategies for hybrid UAVs. In contrast to conventional techniques like fuzzy state machine (FSM)-based control or simple fuzzy logic, which frequently rely on static models or simplified assumptions of flight profiles, this method uses MFRL to predict energy demand in real time while accounting for environmental factors like humidity, temperature, and wind speed. The method optimizes the power distribution between the fuel cell and battery and reduces SoC fluctuations by using a reward function that penalizes the imbalance between the predicted energy demand and the supplied power. This results in an additional 5% fuel cell energy saving (on top of the previous 40% saving) and a 15-min increase in endurance phase (45 min in total), which represents a significant improvement over methods such as FLSM or NMPC, which were reported in previous studies (e.g²⁰. and²³) and achieved 3.1% and 13.3% hydrogen savings, respectively. The integration of the HHO algorithm with MFRL is a significant technical advancement, as it provides the ability to dynamically tune fuzzy logic system parameters and reinforcement learning policies. By optimizing the fuzzy membership functions and MFRL policy coefficients (such as α, β, and γ in Eq. 27), HHO improves the system efficiency in response to environmental uncertainties and minimizes the multi-objective objective function (Eq. 30) that includes DC voltage variations, hydrogen consumption, and endurance. This integration allows for real-time adaptation to environmental changes, which was limited in previous methods such as sequential convex optimization (SCP) or nonlinear model predictive programming (NMPC) due to computational complexity or dependence on predetermined flight data. Simulations performed in MATLAB/Simulink show that this combined approach leads to an 8% reduction in UAV weight and an overall energy saving of 105.43 kJ, demonstrating its superiority over standalone methods such as WHO or FLSM. This improvement, especially in real flight scenarios with random wind speeds (mean 5 m/s, standard deviation 2 m/s), enhances the system’s flexibility and reliability, making it more suitable for long-duration missions.

The main objectives of this study, including increasing endurance, improving energy efficiency, and real-time adaptation to environmental uncertainties, are pursued with specific and measurable criteria in this work. For increasing endurance, simulations in MATLAB/Simulink, based on Table 4 and Fig. 9, show an 8% reduction in the drone weight and an energy saving of 105.43 kJ, resulting in a 45-min increase in the endurance phase (30 min from the initial optimization and an additional 15 min from the MFRL). Also, according to Fig. 12 and Table 6, energy efficiency is measured through a 40% reduction in fuel cell energy consumption and an additional 5% saving with the MFRL, along with a reduction in the SoC fluctuations to 32.5% at the end of the three-hour mission. The energy demand forecasting model (Eq. 27) and HHO-MFRL optimization were used to assess real-time adaptation to environmental uncertainties, such as wind speed variations (mean 5 m/s, standard deviation 2 m/s), which limited the DC voltage variations to less than 1 V (Fig. 13) and decreased the hydrogen consumption to 0.947 kg (Fig. 14).

Analysis of the control framework’s resilience to environmental changes and simulation restrictions

MATLAB/Simulink simulations are used to assess the suggested control framework, which is based on MFRL integrated with fuzzy logic optimized by the HHO algorithm. It is intended to be resilient to real-world environmental variations like wind speed, temperature, and humidity. By integrating dynamic environmental variables (such as wind speed, which has a mean of 5 m/s and a standard deviation of 2 m/s) into the energy demand forecasting model (Eq. 27) and the MFRL reward function (Eq. 28), the framework achieves real-time adaptation. As a result, Fig. 13 shows that DC voltage fluctuations are limited to less than 1 V, and Fig. 14 shows that hydrogen consumption is reduced to 0.947 kg. In response to environmental changes, the HHO optimization modifies the fuzzy membership functions and MFRL policies, leading to a 45-min endurance gain and an energy savings of 105.43 kJ (Results section). Nevertheless, the simulations have drawbacks, such as a lack of validation with actual flight data or more complex environmental circumstances (such high temperature or humidity variations), and they rely on theoretical models and reference data from the literature (^16,17,31). In real-world situations including nonlinear effects or intricate multivariate interactions, these restrictions may reduce the practical usefulness. Future research aims to improve the framework’s practical usability and dependability by incorporating a larger environmental dataset and conducting real flight tests.

The key performance indicators (KPIs) in this study are clearly defined and justified by the main research objectives, namely, increasing endurance, improving energy efficiency, and sustaining the hybrid power system of the fixed-wing UAV. Energy savings (105.43 kJ, reported in the Results section), endurance increase (45 min increase in endurance phase, including 30 min of initial optimization and 15 min of additional MFRL, Table 4 and Fig. 9), battery state of charge (SoC, maintained at 32.5% at the end of the three-hour mission, Fig. 12-b), and fuel cell energy savings (FC, 40% initial reduction and 5% additional with MFRL, Fig. 14) are identified as KPIs. These criteria are aligned with the operational requirements of hybrid UAVs, such as weight reduction (8% reduction, Table 4), minimizing hydrogen consumption (0.947 kg, Fig. 14), and preserving battery and fuel cell life by reducing SoC fluctuations and limiting FC response (Fig. 11). These indicators are evaluated using a dynamic energy demand model (Eq. 27) and HHO-MFRL optimization that considers environmental uncertainties such as wind speed (mean 5 m/s, standard deviation 2 m/s) and are supported by MATLAB/Simulink simulations.

The statistical significance of the results is not directly analyzed in the paper, as the simulations rely on reference data (^16,17,31) and simplifying assumptions (such as constant power profile and linear relationships), and validation with real flight data is not performed. However, the stability of the results is demonstrated by repeating the simulations with the help of the HHO algorithm (Fig. 8) as well as using a dynamic wind model with a specific standard deviation (Fig. 12-a). This approach confirms the consistent improvements in energy savings (105.43 kJ) and endurance increase (45 min) compared to the baseline methods such as FLSM and NMPC (hydrogen savings of 3.1% and 13.3% in²⁰ and²³). However, the lack of formal statistical analysis, such as hypothesis tests or confidence intervals, due to the lack of real experimental data is a limitation mentioned in this section. To improve the statistical significance, future research should include real flight experiments and a wider environmental dataset to assess random variations and nonlinear interactions and strengthen the robustness of the results in practical scenarios.

Because MFRL and HHO are integrated to dynamically modify fuzzy membership functions and power management rules, the proposed MFRL-HHO approach—described in Sections "Multi-Factor Reinforcement Learning (MFRL)" and "Results and discussion"—imposes a substantial computing load. However, by employing fuzzy logic, which is computationally lighter than techniques like nonlinear model predictive control (NMPC) or deep reinforcement learning (DRL), this study has expanded its applicability for resource-constrained UAV systems. The system may be updated every minute, which is compatible with the CPU and memory constraints of UAVs, according to simulations in MATLAB/Simulink with a time scale factor of 1/60 (Section "Results and discussion"). However, as noted in this section, the absence of validation on actual UAV hardware is a drawback, and a thorough computational load analysis (including execution time and memory utilization) is not offered.

Simplifying assumptions and their impact on generalizability

This study has applied several simplifying assumptions to model and simulate the energy management system of a hybrid fuel cell-battery fixed-wing UAV. One of the key assumptions is the use of a predefined mission power profile with five flight phases (takeoff and climb, cruise, endurance, maximum speed, and descent), as described in Table 1 and Fig. 4. This profile assumes that the power demand in each phase is constant or varies linearly, which simplifies the complexities of real flight dynamics such as sudden changes in environmental conditions or nonlinear trajectories. In addition, the propulsion power modeling (Eq. 5) assumes that the lift-to-drag ratio (L/D) is constant, as mentioned in Fig. 2 and reference³¹, while in real flight this ratio can vary due to changes in angle of attack or atmospheric conditions. Also, linear relationships in the energy demand prediction (Eq. 27) are used to account for the effects of wind speed, temperature, and humidity, which may not fully capture the more complex nonlinear interactions in the real world.

These simplifying assumptions, while enabling simulation and simplifying calculations, can limit the generalizability of the results to real flight scenarios. For example, the assumption of a constant or linear power profile may be less accurate in more complex missions with dynamic trajectories or unexpected changes in environmental conditions, such as sudden storms or extreme temperature changes. The assumption of a constant lift-to-drag ratio, as noted in Section "System overview and modeling", may lead to errors in the estimation of propulsive power in situations where the flight dynamics are sensitive to aerodynamic changes, such as rapid maneuvers or flight at different altitudes. In addition, the energy demand prediction model (Eq. 27) with fixed coefficients (α, β, γ) assumes that environmental effects are linearly combined, whereas in reality, these factors may have nonlinear interactions or more complex dependencies. These limitations, as mentioned in Section "Analysis of the control framework’s resilience to environmental changes and simulation restrictions", may reduce the practical applicability of the results in diverse scenarios due to the lack of validation with real flight data and the dependence on reference data (^16,17,31). To mitigate the impact of these assumptions, this study used a dynamic energy demand model (Eq. 27) that takes into account wind speed uncertainty (mean 5 m/s, standard deviation 2 m/s) and employs MFRL and HHO algorithm to dynamically tune parameters, as shown in Figs. 10 and 11. However, to improve generalizability, future research should use real flight data to validate the models and incorporate nonlinear interactions. The intricacies of flight dynamics can also be modeled by using more sophisticated algorithms, such as deep neural networks or deep reinforcement learning (DRL), albeit these techniques demand more processing power. The resilience and practical usability of the suggested framework can be improved by real flight tests and the addition of a larger environmental dataset (such as extreme temperature or humidity variations), enabling its usage in a wider range of missions with varying environmental conditions.

Comparison with other optimization algorithms

The proposed approach in this study, which is based on the combination of MFRL and fuzzy logic optimized with Harris Hawk (HHO) algorithm, has shown remarkable performance in energy management and design optimization of fuel cell-battery hybrid UAVs. This method demonstrates its superiority in MATLAB/Simulink simulations by achieving energy savings of 105.43 kJ, weight reduction of 8%, increased endurance of 45 min, and reduced SoC fluctuations to 32.5% at the end of a three-hour mission, considering wind speed uncertainty (mean 5 m/s, standard deviation 2 m/s). To better evaluate the effectiveness of this approach, its results are compared with widely used optimization algorithms such as GA and PSO. The comparison is based on key criteria including energy savings, weight reduction, endurance enhancement, and SoC stability to highlight the advantages of HHO-MFRL in UAV applications with limited computational resources and dynamic environmental conditions. GA has achieved hydrogen savings of up to 30% in energy management of hybrid battery-super capacitor systems for electric vehicles, but is less suitable for real-time optimization in UAVs due to slower convergence and the need to adjust numerous parameters (such as mutation rate and population size). In contrast, HHO-MFRL, with a higher convergence speed (12 iterations, Fig. 8) and a better balance between exploration and exploitation, offers greater energy savings (105.43 kJ) and a weight reduction of 8%. Similarly, PSO has been reported to achieve 24.1% energy savings over traditional methods such as Gauss Pseudo-spectral for flight path optimization and energy management of hybrid UAVs. However, PSO may get stuck in local optima in high-dimensional problems, while HHO-MFRL, by dynamically adjusting fuzzy membership functions and MFRL policies, provides better performance in flight scenarios with environmental uncertainties. A comparison of these methods is presented in Table 8, which shows the performance of HHO-MFRL against GA and PSO. HHO-MFRL not only provides greater energy savings and endurance, but also improves system stability by limiting DC voltage fluctuations to less than 1 V (Fig. 13) and reducing hydrogen consumption to 0.947 kg (Fig. 14). Although these results are obtained in simulation and need to be validated with real flight data, the superiority of HHO-MFRL in terms of lighter computation and adaptability to environmental changes (such as wind speed) is evident compared to GA and PSO. Future research with real flight experiments and a larger environmental dataset will strengthen this comparison.

Table 8.

Performance comparison of optimization algorithms.

Method	Energy savings	Weight reduction	Endurance increase	SoC fluctuation (end of mission)
HHO-MFRL (Proposed)	105.43 kJ	8%	45 min	32.5%
GA	80.53 kJ (30% hydrogen)	4.6%	23 min	45.2%
PSO	64.36 kJ (24.1% energy)	3.1%	16 min	50.6%

Conclusion and future work

In this work, a fuzzy reinforcement learning system optimized with metaheuristic algorithms has been employed to support a hybrid energy management approach. To plan and schedule the energy consumption of a fixed-wing UAV’s movement using a fuel cell and a battery, we have looked at a fuzzy logic system. In order to develop a really intelligent model for the UAV’s movement that takes into consideration its uncertainties, we have additionally included environmental elements like wind direction and speed. Based on the HHO algorithm, this research suggests an ideal power management and sizing plan for an electric UAV power plant that uses fuel cell batteries. Two distinct profiles were used to evaluate the optimization process: Profile I, which uses constant power steps, and Profile II, which incorporates uncertainties in wind speed and real flight model fluctuations. To get a suitable weight in the first scenario, the ideal sizing—including the ideal battery and fuel cell sizes—is implemented. The optimization process also revealed how the mission’s requirements affected the optimal size of the fuel cell. It is evident from the results that the longest endurance phase power has a significant impact on the FC size. Furthermore, the battery capacity is maintained above 20% at the end of the mission, protecting the battery from deep drain, and the FC response is smooth, both of which are critical for the FC cell lifetime. The inclusion of a totally random wind speed shift along the path for profile 2 aids in realistic simulation. The HHO algorithm has been used in conjunction with the fuzzy logic-based energy management system optimization to determine the fuel cell consumption values during flight and to train the fuzzy reinforcement learning system to establish an energy management between the battery and the fuel cell, which will account for 60% of the fuel cell’s fuel consumption. Our research shows that a fuel cell can significantly boost a UAV’s endurance during the cruise phase, which is often the longest part of flight. During take-off, climb, and sudden variations in load power, the battery is still required to supply extra power. Although the suggested approach necessitates that the load specifications be known beforehand, this study shows the potential advantages of optimizing the fuel cell system and battery capacity, which may improve power performance and offer longer flight times for upcoming UAV missions and weight reduction. In the future, we aim to implement a smart system that utilizes swarm intelligence algorithms. This system will guide the UAV’s movement according to factors such as the speed and direction of the wind at different elevations throughout its geographic course.

Author contributions

All authors contributed to the study conception and design. Data collection, simulation and analysis were performed by Mohsen Rostami, Amirhamzeh Farajollahi and Payman habibi. The first draft of the manuscript was written by Amirhamzeh Farajollahi and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Data availability

The data used in the paper will be available upon request. Please contact a.farajollahi@sharif.edu.

Declarations

Competing interests

The authors declare no competing interests.