Event-Triggered-Based Adaptive Practical Fixed-Time Tracking Control for Uncertain Nonlinear Systems With Unmeasurable States

Lei Liang; Xia Huang; Zhen Wang

doi:10.1109/JAS.2025.125879

Volume 13 Issue 7

Jul. 2026

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 18.3, Top 1 (SCI Q1)

CiteScore: 28.2, Top 1% (Q1)
Google Scholar h5-index: 95， TOP 5

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(7): 1721-1730

L. Liang, X. Huang, and Z. Wang, “Event-triggered-based adaptive practical fixed-time tracking control for uncertain nonlinear systems with unmeasurable states,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 7, pp. 1721–1730, Jul. 2026. doi: 10.1109/JAS.2025.125879

Citation:

L. Liang, X. Huang, and Z. Wang, “Event-triggered-based adaptive practical fixed-time tracking control for uncertain nonlinear systems with unmeasurable states,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 7, pp. 1721–1730, Jul. 2026. doi: 10.1109/JAS.2025.125879

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Event-Triggered-Based Adaptive Practical Fixed-Time Tracking Control for Uncertain Nonlinear Systems With Unmeasurable States

doi: 10.1109/JAS.2025.125879

Funds: This work was supported by the National Natural Science Foundation of China (62573274, 62173214) and the Shandong Provincial Natural Science Foundation (ZR2024MF001)

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Abstract

Abstract

In this paper, the problem of adaptive event-triggered (ET) fixed-time tracking control (FTTC) for a class of uncertain nonlinear systems (NSs) with partially unmeasurable states is investigated. An observer and a set of radial basis function neural networks (RBFNNs) are introduced to reconstruct the unmeasurable states and to approximate the unknown nonlinear functions, respectively. Moreover, in order to reduce the communication resource consumption, an ET mechanism with the relative threshold is adopted. The designed ET controller can ensure that the tracking error converges to a small neighborhood of the origin, all the signals of the closed-loop system are uniformly ultimately bounded (UUB), the settling time depends solely on the design parameters, and the Zeno behavior is successfully avoided. A practical example is given to verify the feasibility of the proposed method.
- Event-triggered (ET) control,
- output feedback,
- practical fixed-time stability,
- uncertain nonlinear systems (NSs),
- unmeasurable states

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References(38)

References

[1]	Y. G. Liu, “Global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and unmeasured states dependent growth,” Sci. China Series F: Inform. Sci., vol. 51, no. 10, pp. 15086–1520, Oct. 2008. doi: 10.3724/sp.j.1004.2009.00272
[2]	X. Yan, Y. Liu, and W. X. Zheng, “Global adaptive output-feedback stabilization for a class of uncertain nonlinear systems with unknown growth rate and unknown output function,” Automatica, vol. 104, pp. 173–181, Jun. 2019. doi: 10.1016/j.automatica.2019.02.040
[3]	F. Shu and J. Zhai, “Global event-triggered output feedback stabilization for a class of nonlinear time-delay systems,” IEEE Trans Circ. Syst. I: Regul. Papers, vol. 68, no. 10, pp. 4371–4380, Oct. 2021. doi: 10.1109/TCSI.2021.3102053
[4]	L. Liang, X. Yan, and T. Shen, “Global output-feedback adaptive stabilization for uncertain nonlinear systems with polynomial growth nonlinearities,” Syst. Control Lett., vol. 165, Art. no. 105269, Jul. 2022. doi: 10.1016/j.sysconle.2022.105269
[5]	W. Liu, Q. Ma, and S. Xu, “Output-feedback adaptive control of a class of uncertain nonlinear systems with dynamic event-triggered strategy,” IEEE Trans. Circ. Syst. II: Express Briefs, vol. 70, no. 12, pp. 4529–4533, Dec. 2023. doi: 10.1109/tcsii.2023.3292175
[6]	B. Li, J. Xia, S. F. Su, W. Sun, and H. Zhang, “Event-triggered adaptive fuzzy tracking control for nonlinear systems with unknown control directions,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 52, no. 7, pp. 4648–4657, Jul. 2022. doi: 10.1109/TSMC.2021.3099808
[7]	W. He, L. Kong, Y. Dong, Y. Yu, C. Yang, and C. Sun, “Fuzzy tracking control for a class of uncertain MIMO nonlinear systems with state constraints,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 49, no. 3, pp. 543–554, Mar. 2019. doi: 10.1109/TSMC.2017.2749124
[8]	Y. Xie and Q. Ma, “Adaptive event-triggered neural network control for switching nonlinear systems with time delays,” IEEE Trans. Neural Netw. Learn. Syst., vol. 34, no. 2, pp. 729–738, Feb. 2023. doi: 10.1109/TNNLS.2021.3100533
[9]	Y. Xie, Q. Ma, and Z. Wang, “Adaptive fuzzy event-triggered tracking control for nonstrict nonlinear systems,” IEEE Trans. Fuzzy Syst., vol. 30, no. 9, pp. 3527–3536, Sep. 2022. doi: 10.1109/TFUZZ.2021.3118732
[10]	A. Bounemeur, M. Chemachema, A. Zahaf, and S. Bououden, “Adaptive fuzzy fault-tolerant control using Nussbaum gain for a class of SISO nonlinear systems with unknown directions,” in Proc. 4th Int. Conf. Electrical Engineering and Control Applications, Constantine, Algeria, 2021, pp. 493−510.
[11]	A. Bounemeur and M. Chemachema, “Adaptive fuzzy fault-tolerant control using Nussbaum-type function with state-dependent actuator failures,” Neural Comput. Appl., vol. 33, no. 1, pp. 191–208, Jan. 2021. doi: 10.1007/s00521-020-04977-6
[12]	A. Bounemeur, M. Chemachema, and N. Essounbouli, “Indirect adaptive fuzzy fault-tolerant tracking control for MIMO nonlinear systems with actuator and sensor failures,” ISA Trans., vol. 79, pp. 45–61, Aug. 2018. doi: 10.1016/j.isatra.2018.04.014
[13]	L. Gao, Z. Song, and Z. Wang, “Command-filter-based finite-time event-triggered adaptive output feedback control for nonlinear systems with state-function constraints,” J. Franklin Inst., vol. 360, pp. 14190–14207, Dec. 2023. doi: 10.1016/j.jfranklin.2023.10.032
[14]	Z. You, F. Wang, and X. Lu, “Event-trigger-based finite-time adaptive fuzzy control for stochastic nonlinear systems with unmeasured states,” IEEE Trans. Fuzzy Syst., vol. 31, no. 12, pp. 4529–4541, Dec. 2023. doi: 10.1109/TFUZZ.2023.3289795
[15]	Q. Yu, X. He, L. Wu, and L. Guo, “Finite-time command filtered event-triggered adaptive output feedback control for nonlinear systems with unknown dead-zone constraints,” Inform. Sci., vol. 617, pp. 482–497, 2022. doi: 10.1016/j.ins.2022.09.008
[16]	A. Bounemeur and M. Chemachema, “Finite-time output-feedback fault tolerant adaptive fuzzy control framework for a class of MIMO saturated nonlinear systems,” Int. J. Syst. Sci., vol. 56, no. 4, pp. 733−752, 2025.
[17]	Q. Meng, Q. Ma, and Y. Shi, “Adaptive fixed-time stabilization for a class of uncertain nonlinear systems,” IEEE Trans. Autom. Control, vol. 68, no. 11, pp. 6929–6936, Nov. 2023. doi: 10.1109/TAC.2023.3244151
[18]	F. Wang and G. Lai, “Fixed-time control design for nonlinear uncertain systems via adaptive method,” Syst. Control Lett., vol. 140, Art. no. 104704, Jun. 2020. doi: 10.1016/j.sysconle.2020.104704
[19]	S. Ling, H. Wang, and P. X. Liu, “Fixed-time adaptive event-triggered tracking control of uncertain nonlinear systems,” Nonlinear Dyn., vol. 100, no. 4, pp. 3381–3397, Jun. 2020. doi: 10.1007/s11071-020-05578-7
[20]	Q. Ma and Y. Xie, “Adaptive event-triggered fixed-time practical tracking control for uncertain nonlinear systems,” IEEE Trans. Autom. Control, vol. 69, no. 8, pp. 5678–5685, Aug. 2024. doi: 10.1109/TAC.2024.3373453
[21]	X. N. Shi, Z. G. Zhou, D. Zhou, and R. Li, “Event-triggered fixed-time adaptive trajectory tracking for a class of uncertain nonlinear systems with input saturation,” IEEE Trans. Circ. Syst. II: Express Briefs, vol. 68, no. 3, pp. 983–987, Mar. 2021.
[22]	Y. Sun, F. Wang, Z. Liu, Y. Zhang, and C. L. P. Chen, “Fixed-time fuzzy control for a class of nonlinear systems,” IEEE Trans. Cybern., vol. 52, no. 5, pp. 3880–3887, May 2022. doi: 10.1109/TCYB.2020.3018695
[23]	K. Lu, Z. Liu, Y. Wang, and C. L. P. Chen, “Fixed-time adaptive fuzzy control for uncertain nonlinear systems,” IEEE Trans. Fuzzy Syst., vol. 29, no. 12, pp. 3769–3781, Dec. 2021. doi: 10.1109/TFUZZ.2020.3028458
[24]	D. Ba, Y. X. Li, and S. Tong, “Fixed-time adaptive neural tracking control for a class of uncertain nonstrict nonlinear systems,” Neurocomputing, vol. 363, pp. 273–280, Oct. 2019. doi: 10.1016/j.neucom.2019.06.063
[25]	X. Song, P. Sun, S. Song, Q. Wu, and J. Lu, “Event-triggered fuzzy adaptive fixed-time output-feedback control for nonlinear systems with multiple objective constraints,” Int. J. Fuzzy Syst., vol. 25, no. 1, pp. 275–288, Feb. 2023. doi: 10.1007/s40815-022-01304-0
[26]	M. Chen, H. Wang, and X. Liu, “Adaptive fuzzy practical fixed-time tracking control of nonlinear systems,” IEEE Trans. Fuzzy Syst., vol. 29, no. 3, pp. 664–673, Mar. 2021. doi: 10.1109/TFUZZ.2019.2959972
[27]	X. Hu, Y. Li, and Z. Hou, “Event-triggered fuzzy adaptive fixed-time tracking control for nonlinear systems,” IEEE Trans. Cybern., vol. 52, no. 7, pp. 7206–7217, Jul. 2022. doi: 10.1109/TCYB.2020.3035779
[28]	J. H. Wang, C. Wang, Z. Liu, C. L. P. Chen, and C. L. Zhang, “Practical fixed-time adaptive ERBFNNs event-triggered control for uncertain nonlinear systems with dead-zone constraint,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 54, no. 1, pp. 342–351, Jan. 2024. doi: 10.1109/TSMC.2022.3211658
[29]	H. Wang, J. Ma, X. Zhao, B. Niu, M. Chen, and W. Wang, “Adaptive fuzzy fixed-time control for high-order nonlinear systems with sensor and actuator faults,” IEEE Trans. Fuzzy Syst., vol. 31, no. 8, pp. 2658–2668, Aug. 2023. doi: 10.1109/TFUZZ.2023.3235395
[30]	Y. Xie, Q. Ma, J. Gu, and G. Zhou, “Event-triggered fixed-time practical tracking control for flexible-joint robot,” IEEE Trans. Fuzzy Syst., vol. 31, no. 1, pp. 67–76, Jan. 2023. doi: 10.1109/TFUZZ.2022.3181463
[31]	H. Xu, D. X. Yu, S. Sui, and C. L. P. Chen, “An event-triggered predefined time decentralized output feedback fuzzy adaptive control method for interconnected systems,” IEEE Trans. Fuzzy Syst., vol. 31, no. 2, pp. 631–644, Feb. 2023. doi: 10.1109/TFUZZ.2022.3184834
[32]	Y. Huang and Y. Liu, “Practical tracking via adaptive event-triggered feedback for uncertain nonlinear systems,” IEEE Trans. Autom. Control, vol. 64, no. 9, pp. 3920–3927, Sep. 2019. doi: 10.1109/TAC.2019.2891411
[33]	C. Zhang and G. Yang, “Event-triggered global finite-time control for a class of uncertain nonlinear systems,” IEEE Trans. Autom. Control, vol. 65, no. 3, pp. 1340–1347, Mar. 2020. doi: 10.1109/TAC.2019.2928767
[34]	L. Xing and C. Wen, “Dynamic event-triggered adaptive control for a class of uncertain nonlinear systems,” Automatica, vol. 158, Art. no. 11286, Dec. 2023. doi: 10.1109/cdc.2018.8619249
[35]	C. Wang, Q. Guo, J. Wang, Z. Liu, and C. L. P. Chen, “Fixed-time fuzzy control for uncertain nonlinear systems with prescribed performance and event-triggered communication,” IEEE Trans. Circ. Syst. I: Regular Papers, vol. 71, no. 5, pp. 2362–2371, May 2024.
[36]	R. Liu, M. Liu, D. Ye, and Y. Yu, “Event-triggered adaptive fixed-time fuzzy control for uncertain nonlinear systems with unknown actuator faults,” Inform. Sci., vol. 612, pp. 344–360, Oct. 2022. doi: 10.1016/j.ins.2022.08.036
[37]	Y. Zhang and F. Wang, “Observer-based fixed-time neural control for a class of nonlinear systems,” IEEE Trans. Neural Netw. Learning Syst., vol. 33, no. 7, pp. 2892–2902, Jul. 2022. doi: 10.1109/TNNLS.2020.3046865
[38]	H. Li, Y. G. Liu, and Y. X. Huang, “Event-triggered controller via adaptive output-feedback for a class of uncertain nonlinear systems,” Int. J. Control, vol. 94, no. 9, pp. 2575−2583, 2021.