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Adaptive Intelligent Control of Nonaffine Nonlinear Time-Delay Systems With Dynamic Uncertainties
Abstract
Adaptive neural intelligent control is investigated for a class of pure-feedback nonlinear time-delay systems with unmodeled dynamics in nonlower-triangular form, which views the lower-triangular structure as a special structure. A variable partition technique is applied to surmount the difficulty in the nonlinear functions of whole state variables. By utilizing the backstepping recursive design approach and the universal approximation capability of neural networks, an adaptive neural controller is systemically designed. Then, based on the utilization of Lyapunov-Krasovskii functionals, the semiglobally uniform boundedness of all closed-loop signals is guaranteed. Finally, the suggested control method is verified through a numerical example. The main advantage of this paper is that an intelligent control method is developed for pure-feedback nonlinear systems with state time delay, unmodeled dynamics and nonlower triangular form. Further developments will focus on how to deal with the problem of output feedback control of pure-feedback nonlinear time-delay systems with unmodeled dynamics and nonlower-triangular structure.
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“Traditional methods based on Lyapunov-Krasovskii functionals are generally less effective in managing input delays compared to state delays [25][26][27].”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [26]
Citations
Cites
Nonlinear and adaptive control design
Krstić, M., Kokotović, P. V., & Kanellakopoulos, I. (1995) · Cited by 10,421
A Robust Adaptive Nonlinear Control Design
Polycarpou, M., & Ioannou, P. A. (1993) · American Control Conference · doi:10.1016/0005-1098(95)00147-6 · Cited by 1,173
Gaussian Networks for Direct Adaptive Control
Sanner, R. M., & Slotine, J.-J. E. (1991) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.1991.4791778 · Cited by 1,079
Liu, Y., & Tong, S. (2016) · Automatica · doi:10.1016/j.automatica.2016.10.011 · Cited by 831
Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form
Zhang, T. P., & Ge, S. S. (2008) · Automatica · doi:10.1016/j.automatica.2007.11.025 · Cited by 754
Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties
Jiang, Z., & Praly, L. (1998) · Automatica · doi:10.1016/s0005-1098(98)00018-1 · Cited by 734
Chen, C. L. P., Wen, G., Liu, Y., & Wang, F. (2014) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2014.2302477 · Cited by 634
Direct adaptive NN control of a class of nonlinear systems
Ge, S. S., & Wang, C. (2002) · IEEE Transactions on Neural Networks · doi:10.1109/72.977306 · Cited by 621
Tong, S., Zhang, L., & Li, Y. (2015) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2015.2426131 · Cited by 541
Liu, Y., Li, J., Tong, S., & Chen, C. L. P. (2016) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2015.2508926 · Cited by 517
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Items 101–151 of 151
Full state constraints-based adaptive control for switched nonlinear pure-feedback systems
Bian, Y., Chen, Y., & Long, L. (2018) · International Journal of Systems Science · doi:10.1080/00207721.2018.1533050 · Cited by 9
Adaptive Control of Nonlinear TRMS Model by Using Gradient Descent Optimizers
Alagöz, B. B., Tepljakov, A., Kavuran, G., & Alisoy, H. Z. (2018) · International Artificial Intelligence and Data Processing Symposium (IDAP) · doi:10.1109/idap.2018.8620807 · Cited by 9
“Intelligent control systems can exhibit the capability of adapting itself for the changing dynamics of real world conditions [1-2].”
BackgroundLi, T., Wang, L., & Li, Z. (2023) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3556 · Cited by 9
“Due to the non-affine property, the mean value theorem in Reference 33 is chosen to design virtual controllers and control laws.”
BackgroundFinite‐time exact tracking control for a class of non‐linear dynamical systems
Hussian, A., Zhao, X., & Zong, G. (2017) · IET Control Theory and Applications · doi:10.1049/iet-cta.2017.0093 · Cited by 9
Mawlani, P., & Arbabtafti, M. (2022) · Transactions of the Institute of Measurement and Control · doi:10.1177/01423312221074181 · Cited by 8
“Dynamic systems based on the control signal dependence are classified into affine (Benosman and Lum, 2009; Phan and Gale, 2008) and non-affine (Ren et al., 2015; Wang et al., 2016) systems.”
BackgroundWang, X., Niu, B., Wu, G., Li, J., Duan, P., & Yang, D. (2018) · IEEE Access · doi:10.1109/access.2018.2884080 · Cited by 7
Shu, Y. (2023) · IET Control Theory and Applications · doi:10.1049/cth2.12221 · Cited by 7
The Irregular Linear Quadratic Control Problem for Deterministic Case with Time Delay
Li, T., Li, L., Lei, J., Jin, N., & Ju, P. (2020) · Journal of Systems Science and Complexity · doi:10.1007/s11424-020-9136-6 · Cited by 6
Zhang, K., Sun, Z., Chen, C., & Meng, Q. (2022) · ISA Transactions · doi:10.1016/j.isatra.2022.06.016 · Cited by 6
Zhang, C., Wang, L., Gao, C., Qu, Q., & Chen, X. (2020) · IEEE Access · doi:10.1109/access.2020.2984344 · Cited by 6
“The mean value theorem in [37] is chosen to solve this difficulty.”
BackgroundOn p-th Moment Exponential Stability for Stochastic Cellular Neural Networks with Distributed Delays
Xu, C., Chen, L., & Li, P. (2018) · International Journal of Control Automation and Systems · doi:10.1007/s12555-017-0570-8 · Cited by 6
Kharrat, M., & Alhazmi, H. (2025) · Neural Processing Letters · doi:10.1007/s11063-025-11749-7 · Cited by 5
Wang, N., Liu, X., Liu, C., Wu, L., Sun, L., & Wang, H. (2025) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2025.3600521 · Cited by 5
“In [7] and [8], the adaptive neural intelligent method was applied to the nonlinear time-delay systems with UDs.”
Self-citationNing, X., Yin, Y., & Wang, Z. X. (2023) · European Journal of Control · doi:10.1016/j.ejcon.2023.100883 · Cited by 5
Study on stability and handling characteristics and control of four-wheel-drive electric vehicles
Huang, F., Fu, C., Tang, X., & Hu, M. (2017) · Advances in Mechanical Engineering · doi:10.1177/1687814017737725 · Cited by 5
Repetitive Learning Control for Control-Affine Systems With Time Delays
Li, H., & Sun, M. (2019) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2019.2946228 · Cited by 5
“In [36] and [37], the time-delay nonlinearities are dealt with, through the backstepping techniques.”
BackgroundCui, E., Jing, Y., & Gao, X. (2017) · Mathematical Problems in Engineering · doi:10.1155/2017/7368092 · Cited by 5
Wang, H., Ping, X., & Wang, X. (2019) · IEEE International Conference on Computational Electromagnetics · doi:10.1109/compem.2019.8779183 · Cited by 4
“(2) In this paper, an output feedback controller based neural networks is proposed for the pure-feedback nonlinear systems with hysteresis nonlinearities and time-delays simultaneously, which is more practical in engineering than the ones in [3]–[8].”
BackgroundSelf-citationL2-gain Analysis and Synthesis of Saturated Switched Linear Systems
Zhang, X., Tao, W., & Su, Q. (2019) · International Journal of Control Automation and Systems · doi:10.1007/s12555-017-0388-4 · Cited by 4
Choi, Y. H., & Yoo, S. J. (2020) · Mathematics · doi:10.3390/math8081341 · Cited by 4
“The choice of the time constants is a general issue in the dynamic surface control approaches (see [3,6,12,18,26,29,31] and the references therein).”
BackgroundAn approach of pondered individual analysis method in aircraft control
Pereira, B. L., Jafelice, R. S. D. M., & Neto, R. M. F. (2022) · Journal of the Brazilian Society of Mechanical Sciences and Engineering · doi:10.1007/s40430-022-03781-8 · Cited by 4
Yue, H., & Wang, H. (2023) · International Journal of Systems Science · doi:10.1080/00207721.2023.2168140 · Cited by 4
“…Sciences, Bohai University, Jinzhou 121000, People’s Republic of China deal with unknown nonlinear terms, so they have been effectively used in nonlinear time-delay systems (C. L. P. Chen et al., 2014; Ge & Tee,2007 ; H. Q. Wang et al., 2015; T. Wang et al.,2017 ; H. Q. Wang et al., 2017).”
BackgroundSelf-citationA Heuristic Task Periods Selection Algorithm for Real-Time Control Systems on a Multi-Core Processor
Fu, H., Liu, J., Han, Z., & Shao, Z. (2017) · IEEE Access · doi:10.1109/access.2017.2768559 · Cited by 4
“Therefore, a lot of work has been focused on control design of time-delay systems, and there have been many interesting results reported in [7]–[10].”
BackgroundYağmur, N., & Alagöz, B. B. (2019) · International Artificial Intelligence and Data Processing Symposium (IDAP) · doi:10.1109/idap.2019.8875966 · Cited by 4
An Optimized Neural Network Classification Method Based on Kernel Holistic Learning and Division
Wen, H., Li, T., Chen, D., Yang, J., & Che, Y. (2021) · Mathematical Problems in Engineering · doi:10.1155/2021/8857818 · Cited by 4
Zhang, B., Zhao, J., Sun, Z., & Hu, Y. (2025) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.70191 · Cited by 3
“To address this, Wang et al. [29] proposed an adaptive intelligent control scheme for non-affine systems, while Chen et al. [30] investigated the coherent control strategy for nonlinear MASs. Similarly, state constraints are another significant issue caused by communication limitations, often due…”
Preparation and adaptive optimization of disposable all-printed urea sensor
Xu, W., Yang, X., Zhao, Y., Fan, M., Liu, J., Pan, P., Yang, Z., Bao, Q., Jin, L., & Liao, Z. (2020) · Journal of Materials Science Materials in Electronics · doi:10.1007/s10854-020-03977-5 · Cited by 3
Zhao, Y. Y., Song, M., Huang, X., & Chen, M. (2021) · Transactions of the Institute of Measurement and Control · doi:10.1177/01423312211058549 · Cited by 3
“In the existing works (Niu et al., 2019; Sanner and Slotine, 1992; Wang et al., 2014, 2017; Yin et al., 2016), the results have shown that, over a compact set O W (cid”
BackgroundSafety control strategy of spinal lamina cutting based on force and cutting depth signals
Zhang, J., Zhang, Y., Liu, S., Ji, X., Liu, S., Li, Z., Geng, B., Li, W., & Wang, T. (2024) · CAAI Transactions on Intelligence Technology · doi:10.1049/cit2.12341 · Cited by 3
Wang, Y., Chen, Z., Sun, M., & Sun, Q. (2018) · IEEE Data Driven Control and Learning Systems Conference (DDCLS) · doi:10.1109/ddcls.2018.8516024 · Cited by 3
“Then adaptive control [4, 5], predictive control algorithm [6], robust control algorithm [7] and various intelligent algorithms [8, 9] appeared, but these algorithms are too complicated to apply in practice.”
MethodWang, D. (2021) · Systems Science & Control Engineering · doi:10.1080/21642583.2021.1949403 · Cited by 3
“Theproblemof adaptiveneural intelligent control was investigated in Wang et al. (2017) for the nonlinear time-delay systems with inmeasurable state.”
BackgroundShu, P., Xie, X., Li, F., Jia, L., Xu, W., & Oya, M. (2024) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3742 · Cited by 2
“30 Therefore, this study utilizes adaptive control algorithms.”
MethodFuzzy Fixed-Time Control for Nonaffine Nonlinear Systems with Unknown Hysteresis Inputs
Li, Y., & Zhao, X. (2023) · International Journal of Fuzzy Systems · doi:10.1007/s40815-023-01556-4 · Cited by 2
“The mean value theorem in [35] is introduced to handle this obstacle.”
BackgroundAdaptive Tracking Control for Uncertain Strict Feedback Systems with Time-Varying Disturbances
Chang, Y. (2025) · Lecture notes in electrical engineering · doi:10.1007/978-981-96-2208-5_46 · Cited by 1
Finite-time adaptive neural output-feedback control of uncertain switched nonlinear systems
Zhang, T., & Zhu, J. (2026) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2026.108438 · Cited by 1
Neural Cognitive Computing Mechanisms
Wang, W., Deng, X., Ding, L., & Zhang, L. (2019) · Research on intelligent manufacturing · doi:10.1007/978-981-13-3549-5_4 · Cited by 1
Zhou, S., Hua, Y., Dong, X., Li, Q., & Ren, Z. (2019) · Advanced Control for Applications · doi:10.1002/adc2.26 · Cited by 1
“(21) Recall that ς(t) = [ξT 1 (t), ξ T 2 (t), .”
Aplicação de Sistemas Neuro-Fuzzy no Controle de Aeronaves em Operações Críticas de Voo
Pereira, B. L. (2021) · doi:10.14393/ufu.te.2021.555 · Cited by 1
Adaptive NN-Based Tracking Control for Partial Uncertain Time-Delayed WMR System
Ding, L., Li, S., Gao, H., Gao, Y., & Deng, Z. (2018) · IEEE International Conference on Real-time Computing and Robotics (RCAR) · doi:10.1109/rcar.2018.8621674
“With the development of the NN-based control algorithms for the strict [4-5], semi-non-strict [6] or non-strict feedback [7] nonlinear systems, several NN-based tracking control methods for the WMR systems had been worked out in recent years [8-12].”
BackgroundMethodEstimator-Based Control for Pure-Feedback Systems With Incomplete Measurements
Wang, L., Liu, X., Chen, X., Li, T., Wei, Y., & Xue, X. (2020) · IEEE Access · doi:10.1109/access.2020.3005913
“In order to design virtual controllers and control laws for affine system by using backstepping method, the mean value theorem is adopted [31].”
MethodAn Inception-Based Architecture for Haemodialysis Time Series Classification
Leonardi, G., Stefania Montani, B., & Striani, M. (2021) · IFIP advances in information and communication technology · doi:10.1007/978-3-030-79157-5_17
Park, J.-S., Oh, S., & Choi, H. (2022) · International Journal of Control Automation and Systems · doi:10.1007/s12555-021-0543-9
Novel deep learning architectures for haemodialysis time series classification
Leonardi, G., Stefania Montani, B., & Striani, M. (2022) · International Journal of Knowledge-based and Intelligent Engineering Systems · doi:10.3233/kes220010 · Cited by 1
Zhai, L.-L., Zhu, S., & Han, Y. (2024) · Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering · doi:10.1177/09596518241233318
“Li et al., 23 Wang et al., 24 and Liu et al. 25 used the Lyapunov-Krasovskii function to compensate for the uncertainty of the unknown time-delay.”
Gao, H., Sun, C., & He, W. (2025) · doi:10.1002/9781394255306.ch1
Gao, H., Sun, C., & He, W. (2025) · doi:10.1002/9781394255306.ref
Adaptive Fault-Tolerant Prescribed Performance Control with Actuator Saturation and Faults
Wei, C., Yin, Z., Wu, X., Wang, Z. X., & Ning, X. (2025) · Springer eBooks · doi:10.1007/978-981-96-3061-5_4
Preliminary Method of Prescribed Performance Control
Wei, C., Yin, Z., Wu, X., Wang, Z., & Ning, X. (2025) · Springer eBooks · doi:10.1007/978-981-96-3061-5_2
Wang, N., Liu, X., Chen, T., Sun, L., & Liu, C. (2026) · Actuators · doi:10.3390/act15020069
Irregular LQ Optimal Control With Multiple Control Inputs and Time Delays
Chen, W., Jin, N., Liu, J., & Yang, Q. (2026) · Optimal Control Applications and Methods · doi:10.1002/oca.70118
“Butcher et al. [25] investigated the adaptive intelligent control problem for non-affine nonlinear systems with time delay and dynamic uncertainties.”
PID-MFAILC Hybrid Speed Regulation for the Rotary Mechanism of Hydraulic Bolt Drills
Zong, L., Liang, J., Bu, X., & Zhang, Y. (2026) · IEEE Data Driven Control and Learning Systems Conference (DDCLS) · doi:10.1109/ddcls71227.2026.11610273
“Other significant contributions include hybrid control methods integrating extended state observers (ESO) [5], adaptive neural intelligent control using variable partitioning [6], and adaptive fuzzy controllers fused with deep reinforcement learning [7].”
Metadata
- Authors
- Wang, H., Sun, W., & Liu, P. X.
- Affiliations
- Carleton University (CA)
- Bohai University (CN)
- Venue
- IEEE Transactions on Systems, Man, and Cybernetics: Systems
- Published
- 2017-07
- Volume
- 47
- Issue
- 7
- Pages
- 1474-1485
- ISSN
- 2168-2216 (ISSN-L)
- 2168-2232
- OpenAlex
- W2558651951
- Cited by
- 151
- References
- 63
- Citations by year
- 2026: 4 · 2025: 10 · 2024: 4 · 2023: 7 · 2022: 14 · 2021: 7 · 2020: 13 · 2019: 20 · 2018: 33 · 2017: 38
- FWCI
- 25.80
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Systems Man and Cybernetics Systems (publishedVersion)
- Funders
- National Natural Science Foundation of China (61304002, 61175072, 61473160)
- Natural Science Foundation of Liaoning Province of China (2015020058)
- 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
- adaptive neural network control, pure-feedback nonlinear systems, time-delay systems, unmodeled dynamics, backstepping control, Lyapunov-Krasovskii functional, state delay
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