Fixed-time filtered backstepping control for quadrotor UAVs with an adaptive fixed-time disturbance observer

Mohammed Rida Mokhtari; Abdelkader Ghezouani; Bensalah Choukri; Amal Choukchou Braham; Hicham Megnafi; Mohammed Rida Mokhtari; Abdelkader Ghezouani; Bensalah Choukri; Amal Choukchou Braham; Hicham Megnafi

doi:10.3934/electreng.2026012

AIMS Electronics and Electrical Engineering

2026, Volume 10, Issue 2: 285-313. doi: 10.3934/electreng.2026012

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Research article

Fixed-time filtered backstepping control for quadrotor UAVs with an adaptive fixed-time disturbance observer

1.
École supérieure en sciences appliquées de Tlemcen, Algeria
2.
Laboratoire d'Automatique de Tlemcen (LAT). Electrical Engineering Department, Tlemcen University, Algeria

Academic Editor: Fanny Spagnolo

Received: 03 February 2026 Revised: 27 February 2026 Accepted: 06 March 2026 Published: 03 April 2026

This work has proposed a novel robust fixed-time tracking control scheme for quadrotor unmanned aerial vehicles subject to unknown external disturbances and model uncertainties. Accounting for the inherent underactuated dynamics of the quadrotor, a hierarchical control architecture was constructed that decouples position and attitude regulation into two separate control loops, namely, an outer loop dedicated to translational motion and an inner loop responsible for rotational dynamics. The proposed framework integrates a fixed-time backstepping design with a command filtering technique to mitigate the explosion-of-complexity problem that typically arises in conventional backstepping approaches, while simultaneously guaranteeing fixed-time convergence of the tracking errors. To effectively address the effects of model uncertainties and external perturbations acting on the system, an adaptive fixed-time disturbance observer was introduced and integrated into the control architecture. This observer is capable of accurately estimating the unknown disturbances and uncertainties, achieving estimation convergence within a predetermined time that remains independent of the initial conditions of the system. Rigorous stability analysis based on Lyapunov theory was carried out to establish the fixed-time convergence of the tracking errors to a bounded neighborhood of the origin. Comprehensive numerical simulations were performed on a quadrotor system, and the results obtained were compared against several existing control methods. The comparative analysis clearly demonstrated that the proposed controller achieves superior tracking accuracy, faster convergence, and improved disturbance rejection performance compared to the alternate approaches considered.
- quadrotor,
- UAV,
- backstepping,
- cascade architecture,
- fixed time,
- disturbance observer,
- adaptive observer,
- nonlinear filter
Citation: Mohammed Rida Mokhtari, Abdelkader Ghezouani, Bensalah Choukri, Amal Choukchou Braham, Hicham Megnafi. Fixed-time filtered backstepping control for quadrotor UAVs with an adaptive fixed-time disturbance observer[J]. AIMS Electronics and Electrical Engineering, 2026, 10(2): 285-313. doi: 10.3934/electreng.2026012

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Abstract

This work has proposed a novel robust fixed-time tracking control scheme for quadrotor unmanned aerial vehicles subject to unknown external disturbances and model uncertainties. Accounting for the inherent underactuated dynamics of the quadrotor, a hierarchical control architecture was constructed that decouples position and attitude regulation into two separate control loops, namely, an outer loop dedicated to translational motion and an inner loop responsible for rotational dynamics. The proposed framework integrates a fixed-time backstepping design with a command filtering technique to mitigate the explosion-of-complexity problem that typically arises in conventional backstepping approaches, while simultaneously guaranteeing fixed-time convergence of the tracking errors. To effectively address the effects of model uncertainties and external perturbations acting on the system, an adaptive fixed-time disturbance observer was introduced and integrated into the control architecture. This observer is capable of accurately estimating the unknown disturbances and uncertainties, achieving estimation convergence within a predetermined time that remains independent of the initial conditions of the system. Rigorous stability analysis based on Lyapunov theory was carried out to establish the fixed-time convergence of the tracking errors to a bounded neighborhood of the origin. Comprehensive numerical simulations were performed on a quadrotor system, and the results obtained were compared against several existing control methods. The comparative analysis clearly demonstrated that the proposed controller achieves superior tracking accuracy, faster convergence, and improved disturbance rejection performance compared to the alternate approaches considered.

References

[1]	Obaid L, Hamad K, Al-Ruzouq R, Abu Dabous S, Ismail K, Alotaibi E (2025) State-of-the-art review of unmanned aerial vehicles (UAVs) and artificial intelligence (AI) for traffic and safety analyses: Recent progress. applications, challenges, and opportunities. IEEE Lat Am T 13: 101591. https://doi.org/10.1109/TLA.2016.7785923 doi: 10.1109/TLA.2016.7785923
[2]	Nahata D, Othman K (2023) Exploring the challenges and opportunities of image processing and sensor fusion in autonomous vehicles: A comprehensive review. AIMS Electronics and Electrical Engineering 7: 271-321. https://doi.org/10.3934/electreng.2023016 doi: 10.3934/electreng.2023016
[3]	Albarghot M, Iqbal MT, Pope K, Rolland L (2020) Dynamic modeling and simulation of the MUN Explorer autonomous underwater vehicle with a fuel cell system. AIMS Electronics and Electrical Engineering 4: 114-131. https://doi.org/10.3934/ElectrEng.2020.1.114 doi: 10.3934/ElectrEng.2020.1.114
[4]	Torres FJ, Guerrero GV, García CD, Gómez JF, Adam M, Escobar RF (2016) Master-Slave Synchronization of Robot Manipulators Driven by Induction Motors. IEEE Lat Am T 42: 3986-3991. https://doi.org/10.1109/TLA.2016.7785923 doi: 10.1109/TLA.2016.7785923
[5]	Bensalah C, Mokhtari MR, Braham AC (2026) A new approach for solving the aerial manipulator inverse kinematics. Journal of the Franklin Institute 362: 107912. https://doi.org/10.1016/j.jfranklin.2025.107912 doi: 10.1016/j.jfranklin.2025.107912
[6]	Mokhtari MR, Braham AC (2016) Disturbance Observer-based Approximate Linearization Control of Gun Launched MAV. Electrotehnica, Electronica, Automatica 64: 131.
[7]	Zeng Y, Yang G, Wang Z (2025) Active disturbance rejection geometric control of quadrotor UAV on SO(3). Journal of the Franklin Institute 362: 107–744. https://doi.org/10.1016/j.jfranklin.2025.107744 doi: 10.1016/j.jfranklin.2025.107744
[8]	Mokhtari MR, Braham AC, Cherki B (2023) Finite-time extended state observer based sliding mode control for a VTOL multi-rotors UAV. IEEE International Workshop on Mechatronic Systems Supervision (IW_MSS), 1–6. https://doi.org/10.1109/IW_MSS59200.2023.10369931
[9]	Wan M, Chen M, Yong K (2022) Adaptive tracking control for an unmanned autonomous helicopter using neural network and disturbance observer. Neurocomputing 468: 296-305. https://doi.org/10.1016/j.neucom.2021.09.060 doi: 10.1016/j.neucom.2021.09.060
[10]	Liu W, Cheng X, Zhang J (2023) Command filter-based adaptive fuzzy integral backstepping control for quadrotor UAV with input saturation. Journal of the Franklin Institute 360: 484-507. https://doi.org/10.1016/j.jfranklin.2022.10.042 doi: 10.1016/j.jfranklin.2022.10.042
[11]	Chávez-Vázquez S, Gómez-Aguilar JF, Lavín-Delgado JE, Escobar-Jiménez RF, Olivares-Peregrino VH (2022) Applications of Fractional Operators in Robotics: A Review. J Intell Robot Syst 104: 63. https://doi.org/10.1007/s10846-022-01597-1 doi: 10.1007/s10846-022-01597-1
[12]	Chen L, Jia Y, Sun S, Lv Z, Wu Y (2025) Immersion and invariance adaptive controller and mixer for coaxial tilt-rotor UAV. ISA Transactions 166: 353-363. https://doi.org/10.1016/j.isatra.2025.07.015 doi: 10.1016/j.isatra.2025.07.015
[13]	Zeghlache S, Rahali H, Djerioui A, Benyettou L, Benkhoris M (2024) Robust adaptive backstepping neural networks fault tolerant control for mobile manipulator UAV with multiple uncertainties. Math Comput Simulat 218: 556-585. https://doi.org/10.1016/j.matcom.2023.11.037 doi: 10.1016/j.matcom.2023.11.037
[14]	Van An V, Mien TL, Van Binh N (2026) A comprehensive survey of UAV control algorithms: Integrating classical methods with artificial intelligence for enhanced trajectory tracking. AIMS Electronics and Electrical Engineering 10: 26-53. https://doi.org/10.3934/electreng.2026002 doi: 10.3934/electreng.2026002
[15]	Chávez-Vázquez S, Gómez-Aguilar JF, Lavín-Delgado JE, Escobar-Jiménez RF, Olivares-Peregrino VH (2022) Intelligent Neural Integral Sliding-mode Controller for a space robotic manipulator mounted on a free-floating satellite. Adv Space Res 71: 3734-3747. https://doi.org/10.1016/j.asr.2022.08.053 doi: 10.1016/j.asr.2022.08.053
[16]	Qin H, Si J, Wang N, Gao L (2023) Fast fixed-time nonsingular terminal sliding-mode formation control for autonomous underwater vehicles based on a disturbance observer. Ocean Eng 270: 113-423. https://doi.org/10.1016/j.oceaneng.2022.113423 doi: 10.1016/j.oceaneng.2022.113423
[17]	Li Y, Liu K, Wen CY, Liu X, Zhang W, Zheng Y (2025) Fast fixed-time incremental backstepping fault-tolerant control for aircraft with asymmetric wing damage. Aerosp Sci Technol 164: 110-405. https://doi.org/10.1016/j.ast.2025.110405 doi: 10.1016/j.ast.2025.110405
[18]	Jiao D, Wang Y, Chen Y, Lu W, Zou AM, Yang X (2025) Finite-time attitude control for fixed-wing UAVs with full-state constraints and input saturation. Journal of the Franklin Institute 362: 107-522. https://doi.org/10.1016/j.jfranklin.2025.107522 doi: 10.1016/j.jfranklin.2025.107522
[19]	Najafi A, Mobayen S, Jalilvand A (2025) Fixed-time anti-saturation and fault-tolerant control for quadrotor UAVs using event-trigger adaptive barrier sliding mode control. ISA Transactions 167: 44-64. https://doi.org/10.1016/j.isatra.2025.08.030 doi: 10.1016/j.isatra.2025.08.030
[20]	Yu B, Du H, Zhu W, Cong Y (2025) A vector-type finite-time trajectory tracking controller for quadrotor UAVs with safety constraints. Aerosp Sci Technol 163: 110-254. https://doi.org/10.1016/j.ast.2025.110254 doi: 10.1016/j.ast.2025.110254
[21]	Guan Z, Liu H, Zheng Z, Lungu M, Ma Y (2021) Fixed-time control for automatic carrier landing with disturbance. Aerosp Sci Technol 108: 106-403. https://doi.org/10.1016/j.ast.2020.106403 doi: 10.1016/j.ast.2020.106403
[22]	Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE T Automat Contr 57: 2106-2110. https://doi.org/10.1109/TAC.2011.2179869 doi: 10.1109/TAC.2011.2179869
[23]	Tran XT, Oh H (2021) A modified generic second-order algorithm with fixed-time stability. ISA Transactions 109: 72-80. https://doi.org/10.1016/j.isatra.2020.10.021 doi: 10.1016/j.isatra.2020.10.021
[24]	Liu Y, An S, Wang L, Fan Z (2025) Predefined time backstepping control with an adaptive predefined time disturbance observer for underactuated AUV under unknown external disturbance. Ocean Eng 340: 122382. https://doi.org/10.1016/j.oceaneng.2025.122382 doi: 10.1016/j.oceaneng.2025.122382
[25]	Xie S, Chen Q (2021) Adaptive nonsingular predefined-time control for attitude stabilization of rigid spacecrafts. IEEE T Circuits-II 69: 189-193. https://doi.org/10.1109/TCSII.2021.3078708 doi: 10.1109/TCSII.2021.3078708
[26]	Mokhtari MR, Bensalah C, Laribi N, Braham AC (2026) Fixed-time observer-based filtered hierarchical control for a gun-launched coaxial rotor vehicle. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 09596518251399967. https://doi.org/10.1177/09596518251399967
[27]	López-Sánchez I, Pérez-Alcocer R, Moreno-Valenzuela J (2023) Trajectory tracking double two-loop adaptive neural network control for a quadrotor. Journal of the Franklin Institute 360: 3770-3799. https://doi.org/10.1016/j.jfranklin.2023.01.029 doi: 10.1016/j.jfranklin.2023.01.029
[28]	Sinan S, Ghommam J, Saad M, Fareh R, Bettayeb M (2025) Cascaded extended-state-observer-based synergetic control for quadcopter translational dynamics. J Field Robot 42: 3153-3171. https://doi.org/10.1002/rob.22566 doi: 10.1002/rob.22566
[29]	Patel N, Paul CK, Kar IN, Mukherjee S (2024) Finite time adaptive backstepping control approach for quadrotors. IFAC-PapersOnLine 57: 89-94. https://doi.org/10.1016/j.ifacol.2024.05.016 doi: 10.1016/j.ifacol.2024.05.016
[30]	Mokhtari MR, Nesserine L (2024) Research on a combinatorial control Method for small aerial vehicles based on disturbance compensation techniques. IEEE International Multi-Conference on Smart Systems & Green Process (IMC-SSGP), 1–6. https://doi.org/10.1109/IMC-SSGP63352.2024.10919745

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