Adaptive NNs‐based 3D trajectory tracking control by state error PCH method for AUVs

Authors

Pei Zhou, Haonan Chen, Yun Chen, Jianjun Bai

Abstract

              This article focuses on the trajectory tracking control (TTC) of autonomous underwater vehicles (AUVs) operating in three‐dimensional (3D) underwater environments with concurrent ocean disturbances, parametric uncertainties and actuator saturation constraints. A tracking control architecture integrating the state‐error port‐controlled Hamiltonian (SEPCH) energy shaping approach with radial basis function neural networks (RBFNNs) is developed to guarantee the uniform ultimate boundedness (UUB) of closed‐loop dynamics. Specifically, the Hamiltonian energy‐shaping framework is systematically synthesized to establish the intrinsic stability property, while adaptive RBFNNs compensators are designed to estimate the compounded perturbations arising from the ocean current disturbances and parameter uncertainties effects. Furthermore, the challenge caused by input saturation is tackled by means of an auxiliary system by confining the control force to certain predefined saturation bounds. Simulation examples demonstrate the validity of the proposed control method.

Citation

• Journal: Asian Journal of Control
• Year: 2026
• Volume:
• Issue:
• Pages:
• Publisher: Wiley
• DOI: 10.1002/asjc.70120

BibTeX

@article{Zhou_2026,
  title={{Adaptive NNs‐based 3D trajectory tracking control by state error PCH method for AUVs}},
  ISSN={1934-6093},
  DOI={10.1002/asjc.70120},
  journal={Asian Journal of Control},
  publisher={Wiley},
  author={Zhou, Pei and Chen, Haonan and Chen, Yun and Bai, Jianjun},
  year={2026}
}

Download the bib file

References

• Cherifi K (2020) An overview on recent machine learning techniques for Port Hamiltonian systems. Physica D: Nonlinear Phenomena 411:132620. https://doi.org/10.1016/j.physd.2020.13262 – 10.1016/j.physd.2020.132620
• Cui R, Chen L, Yang C, Chen M (2017) Extended State Observer-Based Integral Sliding Mode Control for an Underwater Robot With Unknown Disturbances and Uncertain Nonlinearities. IEEE Trans Ind Electron 64(8):6785–6795. https://doi.org/10.1109/tie.2017.269441 – 10.1109/tie.2017.2694410
• Du P, Yang W, Wang Y, Hu R, Chen Y, Huang SH (2022) A novel adaptive backstepping sliding mode control for a lightweight autonomous underwater vehicle with input saturation. Ocean Engineering 263:112362. https://doi.org/10.1016/j.oceaneng.2022.11236 – 10.1016/j.oceaneng.2022.112362
• Elmokadem T, Zribi M, Youcef-Toumi K (2015) Trajectory tracking sliding mode control of underactuated AUVs. Nonlinear Dyn 84(2):1079–1091. https://doi.org/10.1007/s11071-015-2551- – 10.1007/s11071-015-2551-x
• Fan B., Active disturbance observation rejection control based on port‐controlled Hamiltonian with dissipation model for PMSM. Electr. Eng. (2025)
• Fossen TI (2011) Handbook of Marine Craft Hydrodynamics and Motion Contro – 10.1002/9781119994138
• Gheibi A, Ghiasi AR, Ghaemi S, Badamchizadeh MA (2018) Designing of robust adaptive passivity-based controller based on reinforcement learning for nonlinear port-Hamiltonian model with disturbance. International Journal of Control 93(8):1754–1764. https://doi.org/10.1080/00207179.2018.153260 – 10.1080/00207179.2018.1532607
• He W, Yin Z, Sun C (2017) Adaptive Neural Network Control of a Marine Vessel With Constraints Using the Asymmetric Barrier Lyapunov Function. IEEE Trans Cybern 47(7):1641–1651. https://doi.org/10.1109/tcyb.2016.255462 – 10.1109/tcyb.2016.2554621
• Ismail ZH, Mokhar MBM, Putranti VWE, Dunnigan MW (2016) A robust dynamic region-based control scheme for an autonomous underwater vehicle. Ocean Engineering 111:155–165. https://doi.org/10.1016/j.oceaneng.2015.10.05 – 10.1016/j.oceaneng.2015.10.052
• Jia Z, Qiao L, Zhang W (2020) Adaptive tracking control of unmanned underwater vehicles with compensation for external perturbations and uncertainties using Port-Hamiltonian theory. Ocean Engineering 209:107402. https://doi.org/10.1016/j.oceaneng.2020.10740 – 10.1016/j.oceaneng.2020.107402
• Karkoub M, Wu H-M, Hwang C-L (2017) Nonlinear trajectory-tracking control of an autonomous underwater vehicle. Ocean Engineering 145:188–198. https://doi.org/10.1016/j.oceaneng.2017.08.02 – 10.1016/j.oceaneng.2017.08.025
• Khadhraoui A, Beji L, Otmane S, Abichou A (2016) Stabilizing control and human scale simulation of a submarine ROV navigation. Ocean Engineering 114:66–78. https://doi.org/10.1016/j.oceaneng.2015.12.05 – 10.1016/j.oceaneng.2015.12.054
• Kong S, Sun J, Qiu C, Wu Z, Yu J (2021) Extended State Observer-Based Controller With Model Predictive Governor for 3-D Trajectory Tracking of Underactuated Underwater Vehicles. IEEE Trans Ind Inf 17(9):6114–6124. https://doi.org/10.1109/tii.2020.303666 – 10.1109/tii.2020.3036665
• Kumar N, Rani M (2020) An efficient hybrid approach for trajectory tracking control of autonomous underwater vehicles. Applied Ocean Research 95:102053. https://doi.org/10.1016/j.apor.2020.10205 – 10.1016/j.apor.2020.102053
• Lakhekar GV, Waghmare LM, Roy RG (2019) Disturbance Observer-Based Fuzzy Adapted S-Surface Controller for Spatial Trajectory Tracking of Autonomous Underwater Vehicle. IEEE Trans Intell Veh 4(4):622–636. https://doi.org/10.1109/tiv.2019.293808 – 10.1109/tiv.2019.2938082
• Lei M, Li Y, Pang S (2021) Extended state observer-based composite-system control for trajectory tracking of underactuated AUVs. Applied Ocean Research 112:102694. https://doi.org/10.1016/j.apor.2021.10269 – 10.1016/j.apor.2021.102694
• Li B, Gao X, Huang H, Yang H (2024) Improved adaptive twisting sliding mode control for trajectory tracking of an AUV subject to uncertainties. Ocean Engineering 297:116204. https://doi.org/10.1016/j.oceaneng.2023.11620 – 10.1016/j.oceaneng.2023.116204
• Li J, Du J, Chang W-J (2019) Robust time-varying formation control for underactuated autonomous underwater vehicles with disturbances under input saturation. Ocean Engineering 179:180–188. https://doi.org/10.1016/j.oceaneng.2019.03.01 – 10.1016/j.oceaneng.2019.03.017
• Li J, Du J, Chen CLP (2022) Command-Filtered Robust Adaptive NN Control With the Prescribed Performance for the 3-D Trajectory Tracking of Underactuated AUVs. IEEE Trans Neural Netw Learning Syst 33(11):6545–6557. https://doi.org/10.1109/tnnls.2021.308240 – 10.1109/tnnls.2021.3082407
• Li Z, Su C-Y, Wang L, Chen Z, Chai T (2015) Nonlinear Disturbance Observer-Based Control Design for a Robotic Exoskeleton Incorporating Fuzzy Approximation. IEEE Trans Ind Electron 62(9):5763–5775. https://doi.org/10.1109/tie.2015.244749 – 10.1109/tie.2015.2447498
• Li Z, Wang M, Ma G (2023) Adaptive optimal trajectory tracking control of AUVs based on reinforcement learning. ISA Transactions 137:122–132. https://doi.org/10.1016/j.isatra.2022.12.00 – 10.1016/j.isatra.2022.12.003
• Liang X, Zhang Z, Qu X, Li Y, Zhang R (2020) 3D trajectory tracking control of an underactuated AUV based on adaptive neural network dynamic surface. IJVD 84(1/2/3/4):203. https://doi.org/10.1504/ijvd.2020.11586 – 10.1504/ijvd.2020.115864
• Liu J (2013) Radial Basis Function (RBF) Neural Network Control for Mechanical Systems. Springer Berlin Heidelber – 10.1007/978-3-642-34816-7
• Liu S, Liu Y, Liang X, Wang N (2019) Uncertainty observation-based adaptive succinct fuzzy-neuro dynamic surface control for trajectory tracking of fully actuated underwater vehicle system with input saturation. Nonlinear Dyn 98(3):1683–1699. https://doi.org/10.1007/s11071-019-05279- – 10.1007/s11071-019-05279-w
• Luo W., Neural network and disturbance observer‐based practical trajectory tracking of unsymmetric underactuated AUV with disturbance and input saturation. Ships Offshore Struct. (2024)
• Lv C, Yu H, Chen J, Zhao N, Chi J (2022) Trajectory tracking control for unmanned surface vessel with input saturation and disturbances via robust state error IDA-PBC approach. Journal of the Franklin Institute 359(5):1899–1924. https://doi.org/10.1016/j.jfranklin.2022.01.03 – 10.1016/j.jfranklin.2022.01.036
• Lv C, Yu H, Zhao N, Chi J, Liu H, Li L (2020) Robust state‐error port‐controlled Hamiltonian trajectory tracking control for unmanned surface vehicle with disturbance uncertainties. Asian Journal of Control 24(1):320–332. https://doi.org/10.1002/asjc.246 – 10.1002/asjc.2467
• Nicholson JW, Healey AJ (2008) The Present State of Autonomous Underwater Vehicle (AUV) Applications and Technologies. mar technol soc j 42(1):44–51. https://doi.org/10.4031/00253320878686127 – 10.4031/002533208786861272
• Paliotta C, Lefeber E, Pettersen KY, Pinto J, Costa M, de Figueiredo Borges de Sousa JT (2019) Trajectory Tracking and Path Following for Underactuated Marine Vehicles. IEEE Trans Contr Syst Technol 27(4):1423–1437. https://doi.org/10.1109/tcst.2018.283451 – 10.1109/tcst.2018.2834518
• Peng Z, Jiang Y, Wang J (2021) Event-Triggered Dynamic Surface Control of an Underactuated Autonomous Surface Vehicle for Target Enclosing. IEEE Trans Ind Electron 68(4):3402–3412. https://doi.org/10.1109/tie.2020.297871 – 10.1109/tie.2020.2978713
• Sahoo A, Dwivedy SK, Robi PS (2019) Advancements in the field of autonomous underwater vehicle. Ocean Engineering 181:145–160. https://doi.org/10.1016/j.oceaneng.2019.04.01 – 10.1016/j.oceaneng.2019.04.011
• Sarhadi P, Noei AR, Khosravi A (2016) Adaptive integral feedback controller for pitch and yaw channels of an AUV with actuator saturations. ISA Transactions 65:284–295. https://doi.org/10.1016/j.isatra.2016.08.00 – 10.1016/j.isatra.2016.08.002
• Shipra K, Sharma SN, Maurya R (2021) Port-Controlled Hamiltonian Based Controller for Three-Level Ćuk PFC Converter for Battery Charging Application. Electric Power Components and Systems 49(3):276–293. https://doi.org/10.1080/15325008.2021.194306 – 10.1080/15325008.2021.1943067
• Shojaei K (2016) Neural network formation control of underactuated autonomous underwater vehicles with saturating actuators. Neurocomputing 194:372–384. https://doi.org/10.1016/j.neucom.2016.02.04 – 10.1016/j.neucom.2016.02.041
• Sun Z, Wang B, Li Z, Zhao Y, Huang T, Li X, Zhao Y, Qian P, Zhang D (2025) Enhanced trajectory tracking for AUVs: Adaptive Super-Twisting Sliding Mode Control with disturbance observer. Control Engineering Practice 164:106426. https://doi.org/10.1016/j.conengprac.2025.10642 – 10.1016/j.conengprac.2025.106426
• Wang H, Su B (2021) Event-triggered formation control of AUVs with fixed-time RBF disturbance observer. Applied Ocean Research 112:102638. https://doi.org/10.1016/j.apor.2021.10263 – 10.1016/j.apor.2021.102638
• Wang Y, Zhang M, Wilson PA, Liu X (2015) Adaptive neural network-based backstepping fault tolerant control for underwater vehicles with thruster fault. Ocean Engineering 110:15–24. https://doi.org/10.1016/j.oceaneng.2015.09.03 – 10.1016/j.oceaneng.2015.09.035
• Xia Y, Xu K, Li Y, Xu G, Xiang X (2019) Improved line-of-sight trajectory tracking control of under-actuated AUV subjects to ocean currents and input saturation. Ocean Engineering 174:14–30. https://doi.org/10.1016/j.oceaneng.2019.01.02 – 10.1016/j.oceaneng.2019.01.025
• Zhang C, Zou W, Ma L, Cheng N (2024) Port-Hamiltonian modeling and jumping trajectory tracking control for a bio-inspired quadruped robot. Nonlinear Analysis: Hybrid Systems 53:101496. https://doi.org/10.1016/j.nahs.2024.10149 – 10.1016/j.nahs.2024.101496
• Zhang L, Zhang J, Liu S, Ren C, Kang Y (2024) Adaptive Backstepping Fuzzy Lateral Motion Control Approach for Autonomous Vehicles. IEEE Trans Transp Electrific 10(2):4279–4289. https://doi.org/10.1109/tte.2023.330767 – 10.1109/tte.2023.3307671
• Zhang Q, Sun W, Qiao C (2024) Adaptive Fuzzy Control of Switched Port-Controlled Hamiltonian Systems with Input Saturation. Int J Fuzzy Syst 27(2):326–337. https://doi.org/10.1007/s40815-024-01783- – 10.1007/s40815-024-01783-3
• Zhang X, Jiang K (2024) Backstepping-based adaptive control of underactuated AUV subject to unknown dynamics and zero tracking errors. Ocean Engineering 302:117640. https://doi.org/10.1016/j.oceaneng.2024.11764 – 10.1016/j.oceaneng.2024.117640
• Zong G, Wang Y, Niu B, Su S-F, Shi K (2025) Event-Triggered Adaptive NN Tracking Control for Nonlinear Systems With Asymmetric Time-Varying Output Constraints and Application to an AUVs. IEEE Trans Veh Technol 74(1):413–424. https://doi.org/10.1109/tvt.2024.346166 – 10.1109/tvt.2024.3461669