Generalized fault estimator-based prescribed performance control for a class of strict-feedback nonlinear systems

Xuechao Zhang; Shichang Lu; Xuechao Zhang; Shichang Lu

doi:10.3934/math.2025819

AIMS Mathematics

2025, Volume 10, Issue 8: 18337-18355. doi: 10.3934/math.2025819

Previous Article Next Article

Research article Special Issues

Generalized fault estimator-based prescribed performance control for a class of strict-feedback nonlinear systems

Xuechao Zhang ^1,2,
Shichang Lu ^{2
,
,}

1.
School of Economics and Law, University of Science and Technology Liaoning, Anshan, Liaoning, China
2.
School of Business Administration, Liaoning Technical University, Huludao, Liaoning, China

Received: 21 June 2025 Revised: 27 July 2025 Accepted: 06 August 2025 Published: 13 August 2025
MSC : 93D21, 93C10

This paper addresses fault estimation and prescribed performance control for strict-feedback nonlinear systems subject to unknown time-varying faults. By introducing a novel intermediate variable for fault estimation, an adaptive fault estimator and a fault-tolerant controller are proposed. Utilizing a proof by contradiction, the designed prescribed performance control scheme resolves the complex coupling between fault estimation and adaptive control. Furthermore, all closed-loop signals are proven bounded, with both tracking and state errors converging to predesigned compact sets. Finally, numerical simulation on a single-link robot system validates the effectiveness of the proposed algorithm.
- generalized fault estimator,
- prescribed performance control,
- nonlinear system,
- intermediate variable,
- fault-tolerant control
Citation: Xuechao Zhang, Shichang Lu. Generalized fault estimator-based prescribed performance control for a class of strict-feedback nonlinear systems[J]. AIMS Mathematics, 2025, 10(8): 18337-18355. doi: 10.3934/math.2025819

Related Papers:

Abstract

This paper addresses fault estimation and prescribed performance control for strict-feedback nonlinear systems subject to unknown time-varying faults. By introducing a novel intermediate variable for fault estimation, an adaptive fault estimator and a fault-tolerant controller are proposed. Utilizing a proof by contradiction, the designed prescribed performance control scheme resolves the complex coupling between fault estimation and adaptive control. Furthermore, all closed-loop signals are proven bounded, with both tracking and state errors converging to predesigned compact sets. Finally, numerical simulation on a single-link robot system validates the effectiveness of the proposed algorithm.

References

[1]	Y. Yuan, C. Chen, Fault detection of rolling bearing based on principal component analysis and empirical mode decomposition, AIMS Math., 5 (2020), 5916–5938. https://doi.org/10.3934/math.2020379 doi: 10.3934/math.2020379
[2]	Z. Gao, C. Cecati, S. X. Ding, A survey of fault diagnosis and fault-tolerant techniques part Ⅰ: Fault diagnosis with model-based and signal-based approaches, IEEE T. Ind. Electron., 62 (2015), 3757–3767. https://doi.org/10.1109/TIE.2015.2417501 doi: 10.1109/TIE.2015.2417501
[3]	S. X. Ding, Model-based fault diagnosis techniques: Design schemes, algorithms, and tools, Berlin, Germany: Springer-Verlag, 2008. https://doi.org/10.1007/978-3-540-76304-8-7
[4]	Y. Hao, B. Jiang, M. Staroswiecki, Supervisory fault tolerant control for a class of uncertain nonlinear systems, Automatica, 45 (2009), 2319–2324. https://doi.org/10.1016/j.automatica.2009.06.019 doi: 10.1016/j.automatica.2009.06.019
[5]	X. M. Wang, X. D. Zhao, B. Niu, Y. Y. Wang, J. M. Zhang, G. D. Zong, Adaptive fault tolerant tracking control for output constrained nonlinear systems using a novel BLF method, IEEE T. Syst. Man Cy.-S., 55 (2025), 2590–2598. https://doi.org/10.1109/TSMC.2024.3525300 doi: 10.1109/TSMC.2024.3525300
[6]	X. Zhang, L. Liu, Y. J. Liu, Adaptive NN control based on Butterworth low-pass filter for quarter active suspension systems with actuator failure, AIMS Math., 6 (2021), 754–771. https://doi.org/10.3934/math.2021046 doi: 10.3934/math.2021046
[7]	C. Commault, On the disturbed fault detection and isolation problem, Syst. Control Lett., 38 (1999), 73–78. https://doi.org/10.1016/S0167-6911(99)00048-1 doi: 10.1016/S0167-6911(99)00048-1
[8]	S. J. Huang, G. H. Yang, Fault tolerant controller design for T-S fuzzy systems with time-varying delay and actuator faults: A k-step-fault-estimation approach, IEEE T. Fuzzy Syst., 22 (2014), 1526–1540. https://doi.org/10.1109/TFUZZ.2014.2298053 doi: 10.1109/TFUZZ.2014.2298053
[9]	G. H. Yang, H. M. Wang, Fault detection and isolation for a class of uncertain state-feedback fuzzy control systems, IEEE T. Fuzzy Syst., 23 (2015), 139–150. https://doi.org/10.1109/TFUZZ.2014.2308920 doi: 10.1109/TFUZZ.2014.2308920
[10]	M. Rodriguez, H. Hamdi, D. Theilliol, N. B. Braiek, C. Mechmeche, Actuator fault estimation based adaptive polytopic observer for a class of LPV descriptor systems, Int. J. Robust Nonlin., 25 (2015), 673–688. https://doi.org/10.1002/rnc.3236 doi: 10.1002/rnc.3236
[11]	G. Wang, C. Yi, Fault estimation for nonlinear systems by an intermediate estimator with stochastic failure, Nonlinear Dynam., 89 (2017), 1195–1204. https://doi.org/10.1007/s11071-017-3510-5 doi: 10.1007/s11071-017-3510-5
[12]	S. Y. Cheng, H. Yang, B. Jiang, An integrated fault estimation and accommodation design for a class of complex networks, Neurocomputing, 216 (2016), 797–804. https://doi.org/10.1016/j.neucom.2016.08.043 doi: 10.1016/j.neucom.2016.08.043
[13]	X. G. Yan, S. K. Spurgeon, C. Edwards, State and parameter estimation for nonlinear delay systems using sliding mode techniques, IEEE T. Automat. Contr., 58 (2013), 1023–1029. https://doi.org/10.1109/TAC.2012.2215531 doi: 10.1109/TAC.2012.2215531
[14]	K. Zhang, B. Jiang, P. Shi, J. Xu, Analysis and design of robust $H\infty$ fault estimation observer with finite-frequency specifications for discrete-time fuzzy systems, IEEE T. Cybernetics, 45 (2015), 1225–1235. https://doi.org/10.1109/TCYB.2014.2347697 doi: 10.1109/TCYB.2014.2347697
[15]	D. Ichalal, B. Marx, J. Ragot, D. Maquin, Observer based actuator fault tolerant control for nonlinear Takagi-Sugeno systems: An LMI approach, In: 18th Mediterranean Conference on Control and Automation, MED'10, Marrakech, Morocco, 2010, 1278–1283. https://doi.org/10.1109/MED.2010.5547874
[16]	D. Koenig, B. Marx, S. Varrier, Filtering and fault estimation of descriptor switched systems, Automatica, 63 (2016), 116–121. https://doi.org/10.1016/j.automatica.2015.10.017 doi: 10.1016/j.automatica.2015.10.017
[17]	J. Li, S. J. Huang, Integrated observer based fault estimation for a class of Lipschitz nonlinear systems, Int. J. Robust Nonlin., 30 (2020), 5678–5692. https://doi.org/10.1002/rnc.5116 doi: 10.1002/rnc.5116
[18]	J. W. Zhu, G. H. Yang, H. Wang, F. Wang, Fault estimation for a class of nonlinear systems based on intermediate estimator, IEEE T. Automat. Contr., 61 (2016), 2518–2524. https://doi.org/10.1109/TAC.2015.2491898 doi: 10.1109/TAC.2015.2491898
[19]	S. J. Huang, D. Q. Zhang, L. D. Guo, L. B. Wu, Convergent fault estimation for linear systems with faults and disturbances, IEEE T. Automat. Contr., 63 (2018), 888–893. https://doi.org/10.1109/TAC.2017.2735547 doi: 10.1109/TAC.2017.2735547
[20]	A. Zemouche, M. Boutayeb, G. I. Bara, Observer design for nonlinear systems: An approach based on the differential mean value theorem, In: Proceedings of the 44th IEEE Conference on Decision and Control, 2005, 6353–6358. https://doi.org/10.1109/CDC.2005.1583180
[21]	M. Chen, B. Jiang, W. W. Guo, Fault-tolerant control for a class of non-linear systems with dead-zone, Int. J. Syst. Sci., 47 (2016), 1689–1699. https://doi.org/10.1080/00207721.2014.945984 doi: 10.1080/00207721.2014.945984
[22]	Q. Zhou, S. Y. Zhao, H. Y. Li, R. Q. Lu, C. W. Wu, Adaptive neural network tracking control for robotic manipulators with dead zone, IEEE T. Neur. Net. Lear., 30 (2019), 3611–3620. https://doi.org/10.1109/TNNLS.2018.2869375 doi: 10.1109/TNNLS.2018.2869375
[23]	Z. P. Jiang, I. Mareels, D. J. Hill, J. Huang, A unifying framework for global regulation via nonlinear output feedback: From ISS to iISS, IEEE T. Automat. Contr., 49 (2004), 549–562. https://doi.org/10.1109/TAC.2004.825663 doi: 10.1109/TAC.2004.825663
[24]	M. R. Liu, L. B. Wu, M. Wu, W. C. Ma, Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints, Nonlinear Dynam., 113 (2025), 2505–2520. https://doi.org/10.1007/s11071-024-10355-x doi: 10.1007/s11071-024-10355-x
[25]	M. Shen, Y. Ma, H. P. Ju, Q. G. Wang, Fuzzy tracking control for Markov jump systems with mismatched faults by iterative proportional-integral observers, IEEE T. Fuzzy Syst., 30 (2020), 542–554. https://doi.org/10.1109/TFUZZ.2020.3041589 doi: 10.1109/TFUZZ.2020.3041589
[26]	C. C. Wang, G. H. Yang, Prescribed performance adaptive fault-tolerant tracking control for nonlinear time-delay systems with input quantization and unknown control directions, Neurocomputing, 311 (2018), 333–343. https://doi.org/10.1016/j.neucom.2018.05.063 doi: 10.1016/j.neucom.2018.05.063
[27]	X. P. Lin, R. Q. Xu, W. R. Yao, Y. B. Gao, G. H. Sun, J. X. Liu, Observer-based prescribed performance speed control for PMSMs: A data-driven RBF neural network approach, IEEE T. Ind. Inform., 20 (2024), 7502–7512. https://doi.org/10.1109/TII.2024.3357194 doi: 10.1109/TII.2024.3357194
[28]	Y. Z. Sun, J. X. Liu, Y. B. Gao, Z. Liu, Y. Zhao, Adaptive neural tracking control for manipulators with prescribed performance under input saturation, IEEE-ASME T. Mech., 28 (2023), 1037–1046. https://doi.org/10.1109/TMECH.2022.3213441 doi: 10.1109/TMECH.2022.3213441
[29]	J. X. Zhang, G. H. Yang, Prescribed performance fault-tolerant control of uncertain nonlinear systems with unknown control directions, IEEE T. Automat. Contr., 62 (2017), 6529–6535. https://doi.org/10.1109/TAC.2017.2705033 doi: 10.1109/TAC.2017.2705033
[30]	J. X. Zhang, G. H. Yang, Low-complexity tracking control of strict-feedback systems with unknown control directions, IEEE T. Automat. Contr., 64 (2019), 5175–5182. https://doi.org/10.1109/TAC.2019.2910738 doi: 10.1109/TAC.2019.2910738
[31]	Y. Q. Liu, J. P. Liu, J. P. Yu, Singularity avoidance fixed-time adaptive neural control for autonomous underwater vehicles considering unmodelled dynamics and disturbances, IEEE T. Circuits-II, 71 (2024), 822–826. https://doi.org/10.1109/TCSII.2023.3314730 doi: 10.1109/TCSII.2023.3314730
[32]	X. Jin, J. Jiang, J. Qin, W. X. Zheng, M. Gao, Observer-based fixed-time-synchronized control for uncertain Euler–Lagrange systems with bias–actuator faults, IEEE T. Cybernetics, 55 (2025), 3811–3824. https://doi.org/10.1109/TCYB.2025.3576397 doi: 10.1109/TCYB.2025.3576397
[33]	G. G. Yang, J. Y. Yao, Multilayer neurocontrol of high-order uncertain nonlinear systems with active disturbance rejection, Int. J. Robust Nonlin., 34 (2024), 2972–2987. https://doi.org/10.1002/rnc.7118 doi: 10.1002/rnc.7118
[34]	X. Jin, S. Wang, J. Qin, W. X. Zheng, Y. Kang, Adaptive fault-tolerant consensus for a class of uncertain nonlinear second-order multi-agent systems with circuit implementation, IEEE T. Circuits-I, 65 (2018), 2243–2255. https://doi.org/10.1109/TCSI.2017.2782729 doi: 10.1109/TCSI.2017.2782729
[35]	X. Jin, S. Lü, J. Yu, Adaptive NN-based consensus for a class of nonlinear multiagent systems with actuator faults and faulty networks, IEEE T. Neur. Net. Lear., 33 (2022), 3474–3486. https://doi.org/10.1109/TNNLS.2021.3053112 doi: 10.1109/TNNLS.2021.3053112

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)