AccScience Publishing / IJOCTA / Online First / DOI: 10.36922/IJOCTA025450195
Submit to IJOCTA
Cite this article
7
Download
89
Views
Journal Browser
Volume | Year
Issue
Search
Forthcoming Issue
Current Issue
View All
News and Announcements
View All
RESEARCH ARTICLE

Complex variable neural network controller for port-Hamiltonian systems with non-holonomic constraints

Fernando Serrano1 ,  Saim Ahmed2* ,  Ahmad Taher Azar2,3 ,  Ahmed Redha Mahlous2,3
Show Less
1 Institute of Robotics and Industrial Informatics IRI-CSIC, Technical University of Catalonia, Carrer de Llorens i Artigas, 4, Les Corts, Barcelona, Spain
2 Automated Systems and Computing Lab (ASCL), Prince Sultan University, Riyadh, Saudi Arabia
3 College of Computer and Information Sciences, Prince Sultan University, Riyadh, Saudi Arabia
IJOCTA, 025450195 https://doi.org/10.36922/IJOCTA025450195
Received: 5 November 2025 | Revised: 24 February 2026 | Accepted: 27 February 2026 | Published online: 30 April 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Download PDF
XML
Cite
Abstract

This study presents a complex variable neural network (CVNN) controller designed for unmanned aerial vehicles (UAVs) using the port-Hamiltonian formulation with non-holonomic constraints. The approach begins by deriving the dynamic model of a quadrotor UAV in port-Hamiltonian form, where the Hamiltonian is constructed from the system’s total kinetic and potential energies. Dirac structures are implemented to preserve the system’s structural properties while incorporating non-holonomic constraints specifically in the attitude loop. The proposed control architecture decouples the attitude and position control loops, with each utilizing a CVNN controller designed through Lyapunov stability analysis. Theoretical proofs establish the stability of both control loops, while numerical simulations demonstrate the effectiveness of the proposed approach for trajectory tracking tasks. Comparative analysis against existing controllers shows superior performance in reducing root mean square errors while maintaining reasonable control effort. The results confirm that the CVNN controller effectively manages the UAV’s dynamic behavior even with non-holonomic constraints limiting the vehicle’s orientation range.

Graphical abstract
Keywords
Neural networks
Neural control
Port-Hamiltonian systems
Dirac structures
Nonlinear systems
Unmanned aerial vehicles
Funding
This study is supported by a research grant funded by the Research, Development, and Innovation Authority (RDIA) – Kingdom of Saudi Arabia, with grant number (13382-psu-2023-PSNU-R-3-1-EI-). The authors would like to thank Prince Sultan University, Riyadh, Saudi Arabia, for supporting the article processing charges (APC) of this publication.
Conflict of interest
The authors declare no conflict of interest.
References
  1. Pu J, Zhang Q, Zhao W, Zhang W, Qin Z, Zhang Y. Research on refined UAV inspection method of wind/solar power stations based on YOLOv8. J Eng Appl Sci. 2025;72(1). https://www.doi.org/10.1186/s44147-025-00576-1
  2. Li X, Wang A. Forest pest monitoring and early warning using UAV remote sensing and computer vision techniques. Sci Rep. 2025;15(1). https://www.doi.org/10.1038/s41598-024-84464-3
  3. Tarpenning MS, Bramante JT, Coombe KD, et al. Comparison of unmanned aerial vehicle imaging to ground truth walkthroughs for identifying and classifying trash sites serving as potential Aedes aegypti breeding grounds. Parasit Vectors. 2025;18(1). https://www.doi.org/10.1186/s13071-025-06706-1
  4. Xu P, Sulaiman NAA, Ding Y, Zhao J. Innovative segmentation technique for aerial power lines via amplitude stretching transform. Sci Rep. 2025;15(1). https://www.doi.org/10.1038/s41598-025-86753-x
  5. Van Haeften S, Smith D, Robinson H, et al. Unmanned aerial vehicle phenotyping of agro-nomic and physiological traits in mungbean. Plant Phenome J. 2025;8(1). https://www.doi.org/10.1002/ppj2.70016
  6. Li J, Ling M, Fu B, et al. UAV based smart grazing: a  prototype  of  space-air-ground integrated grazing IoT networks in Qinghai-Tibet plateau. Discov IoT. 2025;5(1). https://www.doi.org/10.1007/s43926-025-00114-8
  7. Liller J, Goel R, Aziz A, Hester J, Nguyen P. Development of a battery free, solar powered, and energy aware fixed wing unmanned aerial vehicle. Sci Rep. 2025;15(1). https://www.doi.org/10.1038/s41598-025-90729-2
  8. Han G. Bio-inspired swarm intelligence for en-hanced real-time aerial tracking: integrating whale optimization and grey wolf optimizer algo-rithms. Discov Artif Intell. 2025;5(1). https://www.doi.org/10.1007/s44163-025-00237-5
  9. Liu Y, Zhang H, Zheng H, Li Q, Tian Q. A spherical vector-based  adaptive evolutionary particle swarm optimization for UAV path planning under threat conditions. Sci Rep. 2025;15(1). https://www.doi.org/10.1038/s41598-025-85912-4
  10. Bouzid Y, Siguerdidjane  H,  Bestaoui  Y, Zareb M. Energy Based 3D Autopilot for VTOL UAV Un-der Guidance and Navigation Constraints. J Intell Robot Syst Theory Appl. 2017;87(2):341–362. https://www.doi.org/10.1007/s10846-016-0441-1
  11. Rashad R, Engelen  JBC,  Stramigioli S. Energy   Tank-Based Wrench/Impedance Control of a Fully-Actuated Hexarotor: A Geometric  Port-Hamiltonian  In: 2019 International Conference on Robotics and Automation (ICRA). IEEE ; 2019:6418-6424. https://www.doi.org/10.1109/icra.2019.8793939
  12. Souza C, Raffo GV, Castelan EB. Passivity Based Control of  a  Quadrotor  IFAC-PapersOnLine. 2014;47(3):3196-3201. https://www.doi.org/10.3182/20140824-6-za-1003.02335
  13. Rashad R, Califano  F,  Stramigioli  Port-Hamiltonian  Passivity-Based  Control on  SE(3)  of  a  Fully  Actuated  UAV  for Aerial  Physical  Interaction  Near-Hovering. IEEE Robotics  and  Automation  Letters. 2019;4(4):4378–4385. https://www.doi.org/10.1109/LRA.2019.2932864
  14. Avazzadeh Z, Hassani H, Eshkaftaki AB, Ebadi M, Agarwal P. Optimal solution of nonlinear 2D variable-order fractional optimal control problems using generalized Bessel polynomials. J Vib Control. 2025;31(7-8):1457-1471. https://doi.org/10.1177/10775463241227475
  15. Zhou W, Xu Z, Wu Y, Xiang J, Li Y. Energy-based trajectory tracking control of under-actuated unmanned surface vessels. Ocean Eng. 2023;288. https://www.doi.org/10.1016/j.oceaneng.2023. 116166
  16. Ma L, Pang S, He Y, Wu Y, Li Y, Zhou W. Passivity-Based Sliding Mode Control for the Ro-bust Trajectory Tracking of Unmanned Surface Vessels Under External Disturbances and Model Uncertainty. J Mar Sci Eng. 2025;13(2). https://doi.org/10.3390/jmse13020364 
  17. Lv C, Chen J, Yu H, Chi J, Yang Z. Adaptive NN state error PCH trajectory tracking control for unmanned surface vessel with uncertain-ties and input saturation. Asian J Control. 2023;25(5):3903–3919. https://www.doi.org/10.1002/asjc.3076
  18. Jin L, Yu S, Zhao Q, Shi G, Wu X. Fixed-time H-infinity tracking control  of unmanned underwater vehicles with disturbance rejection via Port-Hamiltonian framework. Ocean Eng. 2024;293. https://www.doi.org/10.1016/j.oceaneng.2023.116533
  19. Wang Z, Zhang Y, Gao Q, Chen J, Lv C. Fourier-Based Formation Control of Multiple Unmanned Surface Vessels Using a State Error Port Control Hamiltonian Framework. In: 2024 China Automation Congress (CAC). IEEE ; 2024:2490-2495. https://www.doi.org/10.1109/cac63892.2024.10865534
  20. Lv C, Wang  Z,  Zhang  Y,  Chen  J,  Yu H. Cooperative formation control of multiple unmanned surface vessels based on state error port control Hamiltonian framework. Ocean Eng. 2024;313. https://www.doi.org/10.1016/j.oceaneng.2024.11941
  21. Feng L, Yu J, Hu C, Yang C, Jiang H. Nonseparation Method-Based Finite/Fixed-Time Synchronization of Fully  Complex-Valued Discontinuous Neural Networks. EEE Trans Cybern. 2021;51(6):3212–3223. https://www.doi.org/10.1109/TCYB.2020.2980684
  22. Jayanthi N, Santhakumari R. Passivity analysis of multiple time-varying time delayed complex vari-able neural networks in finite-time. Math Model Comput. 2021;8(4):842–854. https://www.doi.org/10.23939/mmc2021.04.842
  23. Liu B, Mei X, Jiang H, Wu L. A Nonpenalty Neurodynamic Model for Complex-Variable Optimization. Discrete Dyn Nat Soc. 2021;2021. https://www.doi.org/10.1155/2021/6632257
  24. Sriraman R, Manoj N, Agarwal P, Vigo-Aguiar J, Jain   Event-triggered  control for exponential synchronization of reaction–diffusion fractional-order Clifford-valued delayed neural networks and its application to image encryption. Neurocomputing. 2025;648:130604.  https://doi.org/10.1016/j.neucom.2025.130604
  25. Chen W, Ding Y, Weng F, Liang C, Li J. Global Fast Terminal Fuzzy Sliding Mode Control of Quadrotor UAV Based on RBF Neural Network. Sensors. 2025;25(4). https://www.doi.org/10.3390/s25041060
  26. Xiong JJ, Li C. Neuroadaptive Sliding Mode Tracking Control for an Uncertain TQUAV With Unknown Controllers. Int J Robust Nonlin. 2025;35(2):579–590. https://www.doi.org/10.1002/rnc.7664
  27. Li J, Wu L. A multiple connected recurrent neural network based super-twisting terminal sliding mode control for quad-rotor UAV. Eur J Control. 2025;83. https://www.doi.org/10.1016/j.ejcon.2025.101220
  28. Chai Y, Yang  Z,  Yu  H,  Liang  X,  Han J. Adaptive Trajectory Tracking Control for Double-Pendulum Aerial Transportation System. IEEE Trans Ind Electron. 2025. https://www.doi.org/10.1109/TIE.2025.3536563
  29. Mahmood A, Rehman uF, Okasha M, Saeed A. Neural Adaptive Sliding Mode Control for Camera Positioner Quadrotor UAV. Int J Aeronaut Space Sci. 2025;26(2):733–747. https://www.doi.org/10.1007/s42405-024-00781-x
  30. Li B, Chen M, Qi S, Peng K. Finite-time fault-tolerant control of attitude control system of quadrotor UAV based on neural network disturbance observer. Neural Comput Appl. 2025;37(7):5597–5606. https://www.doi.org/10.1007/s00521-024-10927-3
  31. Wu LF, Wang Z, Rastgaar M, Mahmoudian N. Adaptive velocity control for UAV boat landing: A neural network and particle swarm optimization approach. J Intell Robot Syst. 2025;111(1). https://www.doi.org/10.1007/s10846-024-02201-4
  32. Peng C, Qiao G, Ge B. Dynamic Cascade Spiking Neural Network Supervisory Controller for a Non-planar Twelve-Rotor UAV. Sensors. 2025;25(4). https://www.doi.org/10.3390/s25041177
  33. Zhang Y, Sha H, Peng R, et al. Adaptive Observer-Based Neural Network Control for Multi-UAV Systems with Predefined-Time Stability. Drones. 2025;9(3). https://www.doi.org/10.3390/drones9030222
  34. Bekhiti A, Souanef T, Toubakh H, Horri N, Kafi MR, Bouzid Z. Adaptive UAV Control with Sensor and Actuator Faults Recovery. Aerospace. 2025;12(3). https://www.doi.org/10.3390/aerospace12030261
  35. van der Schaft A, Maschke B. Differential operator Dirac structures. IFAC-PapersOnLine. 2021;54(19):198-203. https://doi.org/10.1016/j.ifacol.2021.11.078
  36. Ye Y, Li Z, Li C, Shen S, Ma WX. A generalized Dirac soliton hierarchy and its bi-Hamiltonian structure. Appl Math Lett. 2016;60:67-72. https://doi.org/10.1016/j.aml.2016.04.010
  37. Yoshimura H, Gay-Balmaz    Dirac structures in nonequilibrium thermodynamics. IFAC-PapersOnline. 2018;51(3):31-37. https://www.doi.org/10.1016/j.ifacol.2018.06.009
  38. Kumar N, Zwart H, van der Vegt J. Dirac structure for linear dynamical systems on Sobolev spaces. J Math Anal Appl. 2025;549(2):129493. https://doi.org/10.1016/j.jmaa.2025.129493
  39. Gay-Balmaz F, Yoshimura H. Variational  and  Dirac  structures  for interconnected  distributed-discrete  IFAC-PapersOnline. 2024;58(6):286-291. https://doi.org/10.1016/j.ifacol.2024.08.295
  40. Tortorella AG. The deformation L-infinity algebra of a Dirac–Jacobi structure. Differential Geometry and its Applications. 2022;80:101846. https://doi.org/10.1016/j.difgeo.2021.101846
  41. Seslija M, van der Schaft A, Scherpen JMA. Reduction of Stokes-Dirac  structures  and gauge symmetry in port-Hamiltonian systems. IFAC-PapersOnLine. 2012;45(19):114-119. https://www.doi.org/10.3182/20120829-3-it-4022.00030
  42. Lamoline F, Hastir A. On Dirac structure of infinite-dimensional stochastic port-Hamiltonian systems. Eur J Control. 2024; 75:100924. https://doi.org/10.1016/j.ejcon.2023.100924
  43. Cervera J, van der Schaft A, Ban˜os A. Interconnection of port-Hamiltonian sys-tems and composition of Dirac structures. Automatica 2007;43(2):212-225. https://doi.org/10.1016/j.automatica.2006.08.014
  44. Azar AT, Serrano FE, Koubaa A, Taha MA, Kamal NA. Fast terminal sliding mode controller for high speed and complex maneuvering of unmanned aerial vehicles. In: Unmanned Aerial Systems. Elsevier; 2021:203-230. https://www.doi.org/10.1016/b978-0-12-820276-0.00016-9
  45. Fujimoto K, Sakai  S,  Sugie    Passivity Hamiltonian  based  control  of  a  class  of systems  with  non-holonomic  Automatica. 2012;48(12):constraints. 3054-3063. https://doi.org/10.1016/j.automatica.2012.08.032
  46. Hui M, Zhang J, Iu HHC, Yao R, Bai L. A novel intermittent sliding mode con-trol approach to finite-time synchroniza-tion of complex-valued neural networks. Neurocomputing. 2022;513: 181-193. https://doi.org/10.1016/j.neucom.2022.09.111
  47. Singha A, Thakur S, Ray AK. Lyapunov based trajectory tracking controller for a quadro-tor UAV with nonholonomic constraints. e-Prime - Advances in Electrical Engineering, Electronics and Energy. 2024;8:100617. https://doi.org/10.1016/j.prime.2024.100617
  48. Shukla A, Arora U, Sukavanam N. Approximate controllability of retarded semilinear stochastic system with non local conditions. Appl Math Comput. 2015;49:513–527. https://doi.org/10.1007/s12190-140851-9
  49. Shukla A, Sukavanam N. Interior approximate controllability of second-order semi-linear control systems. Int J Control. 2024;97(3):615–624. https://www.doi.org/10.1080/00207179.2022. 2161013
  50. Rezapour S, Henr´ıquez HR, Vijayakumar V, Nisar KS, Shukla A. A Note on Existence of Mild Solutions for Second-Order Neutral Integro-Differential Evolution Equations  with State-Dependent Delay. Fractal Fract. 2021;5(3). https://www.doi.org/10.3390/fractalfract5030126
Share
Back to top
An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here
Accept