The DOI matches its Crossref record; 31 of the 31 references it cites were found in a registry or an index.
Adaptive Neural Network‐Based Fixed‐Time Control of Stochastic High‐Order Nonlinear Systems With Unmodeled Dynamics and Multiple Time‐Varying Delays
Abstract
For stochastic nonlinear high‐order systems with unmodeled dynamics together with time‐varying both state and input delays, this paper investigates the fixed‐time tracking control problem for the first time. First, an adaptive neural network‐based controller is designed by integrating the neural network method with adaptive backstepping to solve algebraic loop issues under non‐strict feedback. An improved Lyapunov–Krasovskii function is constructed to compensate for time‐varying state delays, while dynamic and compensation signals are used to handle unmodeled dynamics and input delays, respectively. Then, based on the semi‐global practical fixed‐time stability theory, the boundedness of all signals in the closed‐loop system is proven, demonstrating that the convergence time is independent on system initial values. Finally, simulation examples are given and demonstrate the effectiveness of the devised control scheme.
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“10.1016/j.automatica.2024.111866”
Cited work 10.1016/j.automatica.2024.111866 · retracted 2025-08-21 · notice 10.1016/j.automatica.2025.112471 · this paper published 2026-08-03
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1 retracted
Xie, R. (2024) · Automatica · doi:10.1016/j.automatica.2024.111866 · Cited by 14
RetractedNonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems
Polyakov, A. (2011) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2011.2179869 · Cited by 5,309
Gaussian networks for direct adaptive control
Sanner, R. M., & Slotine, J.-J. E. (1992) · IEEE Transactions on Neural Networks · doi:10.1109/72.165588 · Cited by 2,240
Forward-Backward Stochastic Differential Equations and their Applications
Ma, J., & Yong, J. (2007) · Lecture notes in mathematics · doi:10.1007/978-3-540-48831-6 · Cited by 711
Finite-time stability and instability of stochastic nonlinear systems
Yin, J., Khoo, S., Man, Z., & Yu, X. (2011) · Automatica · doi:10.1016/j.automatica.2011.08.050 · Cited by 543
Adaptive Fuzzy Practical Fixed-Time Tracking Control of Nonlinear Systems
Chen, M., Wang, H., & Liu, X. (2021) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2019.2959972 · Cited by 405
Fuzzy Adaptive Finite-Time Control Design for Nontriangular Stochastic Nonlinear Systems
Sui, S., Chen, C. L. P., & Tong, S. (2019) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2018.2882167 · Cited by 363
Tong, S., Wang, T., & Li, Y. (2013) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2013.2264939 · Cited by 335
Finite-time stabilization of stochastic nonlinear systems in strict-feedback form
Khoo, S., Yin, J., Man, Z., & Yu, X. (2013) · Automatica · doi:10.1016/j.automatica.2013.01.054 · Cited by 318
Finite-time stability theorem of stochastic nonlinear systems
Chen, W., & Jiao, L. (2010) · Automatica · doi:10.1016/j.automatica.2010.08.009 · Cited by 283
Finite-Time Fuzzy Control of Stochastic Nonlinear Systems
Wang, F., Chen, B., Sun, Y., Gao, Y., & Lin, C. (2019) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2019.2925573 · Cited by 252
Hua, C., Ning, P., Li, K., & Guan, X. (2020) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2020.3012560 · Cited by 167
Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems
Yu, X. G., Yin, J., & Khoo, S. (2019) · Automatica · doi:10.1016/j.automatica.2019.05.048 · Cited by 137
Continuous global stabilisation of high-order time-delay nonlinear systems++
Sun, Z., Zhang, X., & Xie, X. (2013) · International Journal of Control · doi:10.1080/00207179.2013.768776 · Cited by 115
Self-citationAdaptive Fuzzy Fixed-Time Decentralized Control for Stochastic Nonlinear Systems
Li, K., Li, Y., & Zong, G. (2020) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2020.3022570 · Cited by 115
Xu, K. W., Wang, H., & Liu, P. X. (2023) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2023.3337792 · Cited by 93
Fixed-Time Lyapunov Criteria of Stochastic Nonlinear Systems and Its Generalization
Min, H., Shi, S., Xu, S., Guo, J. C., & Zhang, Z. (2022) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2022.3218592 · Cited by 91
A Fast Finite-Time Neural Network Control of Stochastic Nonlinear Systems
Wang, F., You, Z., Liu, Z., & Chen, C. L. P. (2022) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2022.3143655 · Cited by 66
Finite-time output feedback stabilization of nonlinear high-order feedforward systems
Zhang, X., Zhang, K., & Xie, X. (2015) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.3384 · Cited by 51
Self-citationGuo, X., Zhang, H., Sun, J., & Zhou, Y. (2022) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2022.3212988 · Cited by 48
Xia, M., & Zhang, T. (2018) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2018.10.011 · Cited by 47
Zhu, Q., & Liu, Y. (2020) · Asian Journal of Control · doi:10.1002/asjc.2321 · Cited by 30
Adaptive Fuzzy Finite-Time Control for a Class of Stochastic Nonlinear Systems with Input Saturation
Sun, W., Gao, M., & Zhao, J. (2021) · International Journal of Fuzzy Systems · doi:10.1007/s40815-021-01107-9 · Cited by 25
Fixed-time tracking control for high-order nonlinear systems with unknown time-varying input delay
Zhai, J., Wang, H., & He, Z. (2023) · Applied Mathematics and Computation · doi:10.1016/j.amc.2023.128027 · Cited by 25
Fuzzy Adaptive Practical Finite-Time Control for Time Delays Nonlinear Systems
Li, K., & Tong, S. (2019) · International Journal of Fuzzy Systems · doi:10.1007/s40815-019-00629-7 · Cited by 24
Yao, Y., Tan, J., Yao, Y., Zhang, X., & Chen, P. (2023) · Neurocomputing · doi:10.1016/j.neucom.2023.127200 · Cited by 24
Self-citationFinite-Time Stability and Stabilization for Continuous Systems with Additive Time-Varying Delays
Lin, X., Liang, K., Li, H., Jiao, Y., & Nie, J. (2016) · Circuits Systems and Signal Processing · doi:10.1007/s00034-016-0443-z · Cited by 22
Zhang, M., & Zhu, Q. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.112391 · Cited by 22
Wei, S.-Y., Li, Y., & Ahn, C. K. (2023) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2023.3321397 · Cited by 15
Yao, Y., Tan, J., Wu, J., & Zhang, X. (2021) · Neural Computing and Applications · doi:10.1007/s00521-021-06210-4 · Cited by 13
Self-citationYao, Y., Tan, J., & Wu, J. (2022) · International Journal of Control Automation and Systems · doi:10.1007/s12555-020-0833-7 · Cited by 6
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Metadata
- Authors
- Zhang, X., Li, F., Liu, E., Zhang, A., & Qiu, J.
- Affiliations
- Linyi University (CN)
- Institute of Intelligent Manufacturing Shandong Traffic Technician College Linyi Shandong People's Republic of China
- Corresponding author
- Zhang, Xinghui
- Venue
- Asian Journal of Control
- Publisher
- Wiley
- Published
- 2026-08-03
- ISSN
- 1561-8625 (ISSN-L)
- 1934-6093
- OpenAlex
- W7172303742
- Cited by
- 0
- References
- 31
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Asian Journal of Control (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Neural Networks Stability and Synchronization
- Keywords
- fixed-time control, nonlinear stochastic systems, high-order nonlinear systems, unmodeled dynamics, time-varying delays, state delay, input delay, adaptive neural network control, adaptive backstepping control, Lyapunov-Krasovskii functional, tracking control
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