Enhanced Disturbance Estimation for Tracking Control of Nonlinear Systems Using Adaptive Fuzzy Finite-Time Observers
DOI:
https://doi.org/10.59247/jfsc.v3i3.348Keywords:
Finite‐Time Disturbance Observer, Fuzzy Logic Control, Adaptive Observer, Nonlinear Control, Disturbance Estimation, Tracking Error, Lyapunov StabilityAbstract
Accurate estimation of unknown and time-varying disturbances is essential for achieving high-performance control of nonlinear systems. This paper investigates the design and comparative evaluation of finite-time disturbance observers with different gain adaptation mechanisms. First, a conventional fixed-gain finite-time disturbance observer and a linearly adaptive finite-time disturbance observer are presented. Then, an adaptive finite-time disturbance observer based on fuzzy logic control is developed to automatically adjust observer gains according to the disturbance estimation error and its rate of change, thereby reducing gain sensitivity and improving transient performance. Finite-time stability of the closed-loop system is rigorously analyzed using Lyapunov theory, and sufficient conditions for convergence are derived. Extensive simulation studies on a nonlinear system subject to high-frequency time-varying disturbances demonstrate the effectiveness of the proposed approach. Quantitative results show that the adaptive finite-time disturbance observer based on fuzzy logic control reduces tracking error and disturbance estimation root mean square error by more than 75% compared with the conventional finite-time disturbance observer and by over 50% compared with the linearly adaptive observer, while yielding smoother control inputs. These results confirm that the adaptive finite-time disturbance observer based on fuzzy logic control significantly enhances robustness and estimation accuracy, making the proposed observer suitable for practical nonlinear control applications under severe disturbance conditions.
References
J. Zhao, D. Feng, J. Cui, and X. Wang, “Finite-Time Extended State Observer-Based Fixed-Time Attitude Control for Hypersonic Vehicles,” Mathematics, vol. 10, no. 17, 2022, https://doi.org/10.3390/math10173162.
M. H. Nguyen and K. K. Ahn, “A Finite-Time Disturbance Observer for Tracking Control of Nonlinear Systems Subject to Model Uncertainties and Disturbances,” Mathematics, vol. 12, no. 22, 2024, https://doi.org/10.3390/math12223512.
L. Gao, G. Zhang, X. Lv, Y. Wang, and Z. Shi, “A Finite-Time Extended State Observer with Prediction Error Compensation for PMSM Control,” Computation, vol. 13, no. 10, 2025, https://doi.org/10.3390/computation13100247.
N. Xuan Mung, N. H. Tiep, L. T. K. Au, N. N. Anh, X. Nguyen, and N. Phi, “A Finite-Time Disturbance Observer-Based Control for Constrained Second-Order Dynamical Systems and Its Application to the Attitude Tracking of a UAV,” Mathematics, vol. 13, no. 11, 2025, https://doi.org/10.3390/math13111810.
B. Ouahab, M. A. Alouane, and F. Boudjema, “Finite-Time Disturbance Observer-based New Fast Terminal Sliding Mode Control for Systems with Uncertainties in Dynamics and Disturbances: Application to Three-DOF Hover Quadrotor,” Unmanned Systems, vol. 13, no. 01, pp. 21–67, 2023, https://doi.org/10.1142/S2301385025500049.
N. Zhang, J. Xia, J. H. Park, J. Zhang, and H. Shen, “Improved disturbance observer-based fixed-time adaptive neural network consensus tracking for nonlinear multi-agent systems,” Neural Networks, vol. 162, pp. 490–501, 2023, https://doi.org/10.1016/j.neunet.2023.03.016.
H. Razmjooei, G. Palli, F. Janabi-Sharifi, and S. Alirezaee, “Adaptive fast-finite-time extended state observer design for uncertain electro-hydraulic systems,” European Journal of Control, vol. 69, 2023, https://doi.org/10.1016/j.ejcon.2022.100749.
Y. Bai, J. Yao, J. Hu, and G. Feng, “Adaptive disturbance observer-based finite-time command filtered control of nonlinear systems,” Journal of the Franklin Institute, vol. 361, no. 14, 2024, https://doi.org/10.1016/j.jfranklin.2024.107095.
E. Ben Alaia, S. Dhahri, and O. Naifar, “Adaptive Observer Design with Fixed-Time Convergence, Online Disturbance Learning, and Low-Conservatism Linear Matrix Inequalities for Time-Varying Perturbed Systems,” Mathematical and Computational Applications, vol. 30, no. 5, 2025, https://doi.org/10.3390/mca30050112.
Z. Li, H. Wei, C. Liu, H. Zhang, Y. Wei, and G. Liu, “A High-Order Finite-Time Observer for External Force Estimation of Collaborative Robots,” International Journal of Robust and Nonlinear Control, vol. 35, no. 8, pp. 2952–2967, 2025, https://doi.org/10.1002/rnc.7816.
K. Guo, C. Wei, and P. Shi, “Fuzzy Disturbance Observer-Based Adaptive Nonsingular Terminal Sliding Mode Control for Multi-Joint Robotic Manipulators,” Processes, vol. 13, no. 6, 2025, https://doi.org/10.3390/pr13061667.
Y. Ren, Y. Sun, and L. Liu, “Fuzzy Disturbance Observers-Based Adaptive Fault-Tolerant Control for an Uncertain Constrained Automatic Flexible Robotic Manipulator,” IEEE Transactions on Fuzzy Systems, vol. 32, no. 3, pp. 1144–1158, 2024, https://doi.org/10.1109/TFUZZ.2023.3319392.
C. Zhao, F. Zhou, and Y. Shen, “Fuzzy observer design for sampled nonlinear systems with measurement uncertainty,” Asian Journal of Control, vol. 26, no. 4, pp. 1939–1951, 2024, https://doi.org/10.1002/asjc.3312.
H. D. Long, “Design of an Indirect Adaptive Controller Based on Fuzzy Logic Control for Linear Cascade Systems Affected by Bounded Unknown Disturbances,” Journal of Fuzzy Systems and Control, vol. 3, no. 3, pp. 174–180, 2025, https://doi.org/10.59247/jfsc.v3i3.320.
N. X. Chiem and N. C. B. Nguyen, “Design of Embedded Control System with Fuzzy Controller and Nonlinear Controller for the Line Follower Robot,” Journal of Fuzzy Systems and Control, vol. 3, no. 2, pp. 122–127, 2025, https://doi.org/10.59247/jfsc.v3i2.303.
P. Chotikunnan, R. Chotikunnan, Y. Pititheeraphab, T. Puttasakul, A. Wongkamhang, and N. Thongpance, “Comparative Analysis of Fuzzy Membership Functions for Step and Smooth Input Tracking in a 3-Axis Robotic Manipulator,” Journal of Fuzzy Systems and Control, vol. 3, no. 1, pp. 39–50, 2025, https://doi.org/10.59247/jfsc.v3i1.278.
V.-H.-L. Tran et al., “Backstepping Control for Ball and Beam: Simulation and Experiment,” Journal of Fuzzy Systems and Control, vol. 3, no. 1, pp. 30–38, 2025, https://doi.org/10.59247/jfsc.v3i1.275.
X. Liu, Y. Zhang, S. Xiong, L. Du, and Y. Li, “An extended state observer for a class of nonlinear systems with a new frequency-domain analysis on convergence,” ISA Transactions, vol. 107, pp. 107–116, 2020, https://doi.org/10.1016/j.isatra.2020.07.035.
T. N. Ma, R. D. Xi, X. Xiao, and Z. X. Yang, “Nonlinear Extended State Observer Based Prescribed Performance Control for Quadrotor UAV with Attitude and Input Saturation Constraints,” Machines, vol. 10, no. 7, 2022, https://doi.org/10.3390/machines10070551.
T. Li, H. Xing, E. Hashemi, H. D. Taghirad, and M. Tavakoli, “A brief survey of observers for disturbance estimation and compensation,” Robotica, vol. 41, no. 12, pp. 3818–3845, 2023, https://doi.org/10.1017/S0263574723001091.
Y. Sun, J. Huang, and T. Ge, “Autonomous finite-time disturbance observer-based control of the micro turbine: Speed/frequency regulation and dynamic power compensation,” Aerospace Traffic and Safety, vol. 2, no. 1, pp. 28–34, 2025, https://doi.org/10.1016/j.aets.2025.04.003.
Y. Wu, F. Ma, X. Yang, S. Wang, and X. Liu, “Fixed-Time Disturbance Observer-Based Adaptive Finite-Time Guidance Law Design considering Impact Angle Constraint and Autopilot Dynamics,” Complexity, vol. 2021, no. 1, 2021, https://doi.org/10.1155/2021/8735625.
J. Zhang and S. Tong, “Observer-Based Fuzzy Adaptive Formation Control for Saturated MIMO Nonlinear Multiagent Systems Under Switched Topologies,” IEEE Transactions on Fuzzy Systems, vol. 32, no. 3, pp. 859–869, 2024, https://doi.org/10.1109/TFUZZ.2023.3308122.
R. Miranda-Colorado and N. R. Cazarez-Castro, “Observer-based fuzzy trajectory-tracking controller for wheeled mobile robots with kinematic disturbances,” Engineering Applications of Artificial Intelligence, vol. 133, 2024, https://doi.org/10.1016/j.engappai.2024.108279.
A. Saibi, R. Boushaki, and H. Belaidi, “Backstepping Control of Drone,” Engineering Proceedings, vol. 14, no. 1, 2022, https://doi.org/10.3390/engproc2022014004.
X.-J. Liu and X.-X. Zhou, “Structural analysis of fuzzy controller with gaussian membership function,” in IFAC Proceedings Volumes, 1999, pp. 5368–5373, https://doi.org/10.1016/s1474-6670(17)56914-1.
J. Zhao and B. K. Bose, “Evaluation of membership functions for fuzzy logic-controlled induction motor drive,” in IECON Proceedings (Industrial Electronics Conference), 2002, pp. 229–234, https://doi.org/10.1109/iecon.2002.1187512.
W. Wang and Y. Lu, “Analysis of the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE) in Assessing Rounding Model,” in IOP Conference Series: Materials Science and Engineering, 2018 https://doi.org/10.1088/1757-899X/324/1/012049.
T. Chai and R. R. Draxler, “Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature,” Geoscientific Model Development, vol. 7, no. 3, pp. 1247–1250, 2014, https://doi.org/10.5194/gmd-7-1247-2014.
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