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Adaptive Finite-Time Tracking Control of Nonlinear Systems With Dynamics Uncertainties
Abstract
In this article, the problem of adaptive backstepping finite-time tracking control is investigated for a class of strict-feedback nonlinear systems with unmodeled dynamics and dynamic disturbances. A modified finite-time dynamic signal is first introduced to dominate the dynamic disturbance. By using the adaptive control, backstepping technique, and finite-time stability theory, an adaptive finite-time tracking controller is developed. Under the proposed control scheme, the finite-time tracking performance and the boundedness property of all signals in the closed-loop system are ensured. Finally, simulation results check the effectiveness of the suggested approach.
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“Additionally, a significant limitation of traditional adaptive finite-time control methods is their dependency on initial conditions, which makes it difficult to predict the settling time in advance.”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [38]
In the citing paper
“This work overcomes the prevailing limitations associated with convergence time dependence on initial states in [38,39] by devising a fixed-time controller.”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [38]
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Liu, Y., & Hao, L. (2024) · Applied Mathematics and Computation · doi:10.1016/j.amc.2024.128666 · Cited by 10
Yan, S., Xia, Y., & Zhai, D. (2024) · International Journal of Systems Science · doi:10.1080/00207721.2024.2328065 · Cited by 10
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Wang, H., Yang, D., Zong, G., Zhao, X., & Shi, K. (2024) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2024.3405568 · Cited by 10
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MethodSelf-citationPredefined‐time tracking control of a class of nonlinear systems via a novel C∞ performance function
Li, J., & Du, J. (2023) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7152 · Cited by 9
Adaptive finite‐time fuzzy secure control for nonlinear MASs under deception attacks
Bai, Z., Bi, W., Sui, S., Tong, S., & Chen, C. L. P. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7286 · Cited by 9
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MethodFree-Will Arbitrary Time Adaptive Control for Uncertain Lorenz System
Wang, H., Jiang, W., & Shen, H. (2023) · IEEE Transactions on Circuits & Systems II Express Briefs · doi:10.1109/tcsii.2023.3302305 · Cited by 9
“Thus, since Weiss and Infante [10] first reported finite-time stability theory, finite-time control has accepted increasing attention by both theoreticians [11] and practitioners [12].”
BackgroundSelf-citationChen, J., Li, J., Chen, W., & Gao, W. (2023) · Science China Technological Sciences · doi:10.1007/s11431-023-2464-1 · Cited by 8
Zhang, H., Liu, X., Sun, J., & Yue, X. (2025) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2025.3603637 · Cited by 8
“Furthermore, unlike the finite-time scheme in [13], the proposed practical fixed-time scheme guarantees that the control period is independent of the initial state of the system.”
Self-citationHuang, Z., Li, T., Long, Y., Yang, H. C., Chen, C. L. P., & Liang, H. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7207 · Cited by 8
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Adaptive Iterative Learning Control for Nonlinear Multiagent Systems With Initial Error Compensation
Li, Z., Zhou, Q. F., Liu, Y., Ren, H., & Li, H. (2024) · IEEE Transactions on Artificial Intelligence · doi:10.1109/tai.2024.3366877 · Cited by 8
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BackgroundShi, W., Liu, J., Lam, H., & Yu, J. (2024) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2024.3496781 · Cited by 7
“In the last few decades, a number of remarkable achievements have been made for state immeasurable systems [1], [2], [3], [4], [5], [6], [7].”
Adaptive predefined-time tracking control of nonlinear systems with unmodeled dynamics
Ai, Z., & Wang, H. (2025) · International Journal of Control · doi:10.1080/00207179.2025.2479185 · Cited by 7
Self-citationYue, X., Zhang, H., & Ma, J. (2025) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2025.3611950 · Cited by 7
“A finite-time adaptive tracking controller was developed in [22] for nonlinear systems with unmodeled dynamics and dynamic disturbances.”
Self-citationNussbaum-Based Fixed-Time Adaptive Fault-Tolerant Control and Its Application to Robot Manipulator
Cheng, S., Wang, Q.-G., Yu, J., & Liu, J. (2026) · IEEE Transactions on Consumer Electronics · doi:10.1109/tce.2026.3651711 · Cited by 7
“To ensure system control performance, it is necessary to investigate nonlinear control methods [6], [7], [8].”
Finite-Time Fault-Tolerant Control for a Coaxial Tilt-Rotor eVTOL Under a Rotor Fault
Hou, Z., Lv, Z., Wu, Y., & Zhou, H. (2026) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2026.3661006 · Cited by 7
“As we know, finite-time control has been widely researched due to its advantages of enhanced tracking precision, stronger robustness, and improved transient performance [22], [23], [24].”
Kang, S., Liu, P. X., & Wang, H. (2023) · Asian Journal of Control · doi:10.1002/asjc.3204 · Cited by 7
“To this day, the theoretical study results of tracking control problem have been dramatically reported; see [14–18].”
BackgroundSelf-citationWang, K. X., Wen, S.-X., Gao, Y., Zhang, X., & Sun, X. (2023) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2023.3346803 · Cited by 7
“However, due to physical limitations and safety requirements, the actuator output and its rate cannot be arbitrarily large [1], [2], [3].”
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“Subsequent studies [17], [18], [19], [20], [21], [22], [23], [24] have successfully eliminated these nonlinear growth conditions and established criteria for semi-global practical finite-time stability (SGPFS).”
Probabilistic Model-Based Fault-Tolerant Control for Uncertain Nonlinear Systems
Zhao, L., Wen, G., Guo, Z., Zhu, S., Hu, C., & Wen, S. (2025) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2025.3539464 · Cited by 7
“However, existing studies [14], [15] tend to be conservative, and approximation methods [16], [17] struggle to address scenarios where system states are affected by noise disturbances and imperfect measurements.”
Kharrat, M. (2025) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.4007 · Cited by 6
“While the method in [35] is limited to addressing actuator faults, the proposed approach extends its applicability by incorporating both actuator faults and asymmetric dead-zone nonlinearity within an event-triggered finite-time adaptive con-trol framework.”
InfluentialEvent-Based Adaptive PI-Funnel Global Tracking Control for Uncertain Nonlinear Systems
Zhang, C., Hu, Z. S., Li, Y.-J., Zhang, Y., Hua, C., & Liu, Y.-Y. (2025) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2025.3605859 · Cited by 6
“I N RECENT decades, the tracking control of nonlinear systems under transient and steady-state constraints has been an important research topic, with work including finite-time tracking control [1], [2], [3] and prescribed performance tracking control [4], [5], [6], [7], [8].”
Tan, T., Zhuang, S., & Shi, Y. (2024) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2024.3422871 · Cited by 6
“With the growing demands for reliability and adaptability in practical engineering, resilient and robust control synthesis of switched systems is urgently required in the complex industrial environment [15].”
Su, Y., Shen, S., Hu, Z., & Li, Z. (2024) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2024.3486679 · Cited by 6
A novel flexible fixed-time stability result and its application in sliding-mode controller design
Cao, Y., Wen, H., Zhang, X., Zhou, H., Yao, B., & Lian, L. (2025) · Nonlinear Dynamics · doi:10.1007/s11071-025-11035-0 · Cited by 6
“Finite-time stability guarantees that the system converges to a stable state within a finite time, offering significant advantages in practical applications [4–6].”
Yang, J., Wang, X., Xu, C., Yu, Y., & Guo, T. (2024) · Mechatronics · doi:10.1016/j.mechatronics.2024.103168 · Cited by 6
Kharrat, M., & Alhazmi, H. (2025) · Neural Processing Letters · doi:10.1007/s11063-025-11749-7 · Cited by 5
Xue, L., Liu, G. P., & Hu, W. (2024) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2024.3379279 · Cited by 5
“…for microgrids [9], [10], diagnosis, detection, and prognosis for power systems of ships [11], [12], computer-aided detection of detecting infectious disease [13], [14], tracking control of nonlinear systems [15], [16], consumption reduction of rail transit energy [17], decision making [18], etc.”
BackgroundYu, X., & Li, X. (2024) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2024.3460749 · Cited by 5
“It is well known that the finite-time [21], [22] or fixed-time [11], [12] stabilization can ensure convergence within finite time.”
Kharrat, M., & Alhazmi, H. (2024) · Journal of low frequency noise, vibration and active control · doi:10.1177/14613484241285490 · Cited by 5
“34 Recently, there has been considerable emphasis on the development and evaluation of fi nite-time control.”
Li, Z., Chen, H., Wu, W., Jia, Z., & Zhang, W. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7765 · Cited by 5
“…stability has attracted considerable attention and achieved many significant results due to its finite-time convergence for practical control systems, such as the electro-hydraulic servo system [33], the complex dynamical networks [34], the pendulum system [35], and the vehicle system [36].”
Kumar, B. R., & Balasubramaniam, P. (2025) · Nonlinear Dynamics · doi:10.1007/s11071-024-10853-y · Cited by 5
Free-will arbitrary time backstepping control for a class of nonlinear systems with disturbance
Jiang, W., & Wang, H. (2025) · Journal of Control and Decision · doi:10.1080/23307706.2025.2546568 · Cited by 5
Self-citationWang, 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
“Some other researches about UDs are shown in [13], [14], [15], and [16].”
Self-citationGolestani, M., Song, Y., Liu, W., Duan, G., & Kong, H. (2026) · Automatica · doi:10.1016/j.automatica.2026.112902 · Cited by 5
Finite‐time H∞ filtering for Markov jump systems with partially unknown transition rates
Zhou, J., & Ai, X. (2024) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3900 · Cited by 5
Finite- and Fixed-Time Learning Control for Continuous-Time Nonlinear Systems
Li, Z., Shen, D., & Ho, D. W. C. (2024) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2024.3488961 · Cited by 5
“This is because, for the adaptive control strategy in [15], the control objective is to achieve finite-time control rather than estimate unknown parameters.”
InfluentialJiang, W., Wang, H., & Wang, W. (2023) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3598 · Cited by 5
“̂ W1 = Γ1(X1S1 + e1S1) − σ1̂ W1, (30) ?̇?1 = −K11γ1 + γ2 + ω2 − α1 − ι1sign(γ1), (31) where the constants σ1 > 0 and ι1 > 0.”
MethodSelf-citationWang, M., Han, T., Xiao, B., & Yan, H. (2023) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3698 · Cited by 5
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“Therefore, the next step should consider combining finite-time [59] and fixed-time [60] stability theories to design an adaptive fault compensation controller for nonlinear systems with intermittent actuator failures.”
Zhang, J., Yan, C., Xia, J., Shen, H., & Xie, X. (2024) · Information Sciences · doi:10.1016/j.ins.2024.120717 · Cited by 5
Finite-time PID control for nonlinear nonaffine systems
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“Meanwhile, the FTS of nonlinearly parameterized systems [38,39] and the neural network FTC [40,41] have been studied, for example, the novel results on the fuzzy adaptive fixed-time quantized feedback control [42] and the adaptive finite-time tracking control [43] of nonlinear systems.”
Disturbance observer-based fuzzy adaptive optimal finite-time control for nonlinear systems
Sun, Z., Liang, L., & Gao, W. D. (2023) · Applied Mathematics in Science and Engineering · doi:10.1080/27690911.2023.2199211 · Cited by 5
Lin, J., Wang, M., Yan, H., & Yang, W. D. (2025) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2025.107881 · Cited by 4
Liu, W., Ma, Q., & Xu, S. (2025) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2025.3590546 · Cited by 4
“Especially for tracking control of nonlinear systems with disturbances [29], [30], The tracking error is frequently uniformly bounded.”
Kharrat, M., & Mercorelli, P. (2025) · Mathematics · doi:10.3390/math14010030 · Cited by 4
Ma, L., Wang, Z., & Huang, C. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7355 · Cited by 4
“First method is to use the bound of g directly if the interval bounds are known, such as References 2–5,12,18,30,33,40.”
MethodJiang, W., Wen, G., & Ge, S. S. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7634 · Cited by 4
“6 In addition to constraints, 7–9 many practical systems suffer from uncertainties, such as model uncertainties 10,11 and disturbances.”
Liu, Y., Sun, Y., & Hao, L. (2025) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2025.3574160 · Cited by 4
“Next, to dispose of the dynamic disturbance and realize tracking objective in finite-time for nonlinear systems, an adaptive controller was devised in [14].”
Wang, B., Tang, J., Tian, H., Yu, W., & Qiao, J. (2025) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2025.3590654 · Cited by 4
“Adaptive control methods can address time-varying dynamics, but they can be computationally expensive and may not guarantee stability in the presence of significant uncertainties [30].”
Xu, K. W., Wang, H., & Liu, P. X. (2023) · International Journal of Systems Science · doi:10.1080/00207721.2023.2228809 · Cited by 4
“With the actual industrial system becomes more complex (M. Wang et al., 2020, 2022; X. Xie, Qiu, et al., 2023; X. Xie, Xu, et al.,2022 ), compared with the single-agent systems, the multi-agent systems (MASs) have stronger practical significance, which usually are mostly utilised to model…”
BackgroundSelf-citationSupervisory-based quantised hands-off control for a class of uncertain systems with nonlinear sector
Singh, S., Sachan, A., Goyal, J. K., Purwar, S., & Soni, S. (2023) · International Journal of Systems Science · doi:10.1080/00207721.2023.2271118 · Cited by 4
“For this, adaptive controllers (Wang, Tong, et al., 2023; Wang, Xu, et al., 2023) are designed in a manner that the over-all variation in system dynamics is automatically compensated by adjusting the process parameters to maintain optimum performance.”
BackgroundPractical prescribed‐time tracking control of unknown nonlinear systems: A low‐complexity approach
Xie, H., Zhang, J., Jing, Y., Chen, J., & Dimirovski, G. M. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7555 · Cited by 4
“10,11 Nevertheless, it should be pointed out that the settling time of finite-time control is dependent on the initial condition.”
InfluentialAn Accelerated Adaptive Gain Design in Stochastic Learning Control
Cheng, X., Jiang, H., Shen, D., & Yu, X. (2024) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2024.3440261 · Cited by 4
“In [20], an adaptive backstepping tracking control scheme is specifically developed for nonlinear systems with dynamic uncertainties.”
Dual‐channel observer design for composite disturbances based on characteristic compensation
Wen, X., Wang, Z., Dong, Y., & Li, R. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7636 · Cited by 4
Wang, C., Guo, Q., Zhan, H., Li, W., & Li, T. (2025) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2025.108808 · Cited by 4
Distributed online optimisation in unknown dynamic environment
Wang, S., & Huang, B. (2024) · International Journal of Systems Science · doi:10.1080/00207721.2024.2302903 · Cited by 4
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BackgroundXu, K. W., Wang, H., & Liu, P. X. (2024) · Nonlinear Dynamics · doi:10.1007/s11071-024-09717-2 · Cited by 4
Self-citationKang, S., Liu, P. X., & Wang, H. (2023) · International Journal of Systems Science · doi:10.1080/00207721.2023.2210147 · Cited by 4
Self-citationLiu, L., Zhang, L., Wu, S., & Fang, Y. (2025) · International Journal of Control · doi:10.1080/00207179.2025.2460042 · Cited by 3
“Over the past few decades, the research of nonlinear systems has achieved rapid development due to their great significance both in theory and practice (Song et al., 2017; Sun et al., 2020; Wang et al., 2023).”
Consensus Control Strategy for the Treatment of Tumour with Neuroadaptive Cellular Immunotherapy
Sun, J., Li, D., Zhang, H., Liu, L., & Zhao, W. (2025) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2024.124941 · Cited by 3
Self-citationAdaptive Prescribed-Time Control of Switched Nonlinear Systems With False Data Injection Attacks
He, W., Shi, Y., & Wang, Y. (2025) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2025.3568861 · Cited by 3
“In contrast to the traditional asymptotic control [18], [19], [20], finite-time control can drive the system state to a desired region in a finite time and has yielded rich research results [21], [22], [23].”
Fang, L., Shen, H., Wang, H., & Song, T. (2025) · ISA Transactions · doi:10.1016/j.isatra.2025.07.041 · Cited by 3
Self-citationLiu, X., Wang, N., Liu, C., Chen, T., & Sun, L. (2025) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2025.3637301 · Cited by 3
“To this end, inspired by [28], su ffi ciently di ff erentiable piecewise functions are proposed for the virtual controller design.”
Adaptive control of uncertain output-feedback systems with time-varying actuator faults
Ma, Z., Wang, Q., Wang, B., & An, B. (2026) · Applied Mathematical Modelling · doi:10.1016/j.apm.2026.116826 · Cited by 3
Jiang, H., Yin, L., Sun, Z., Mu, C., & Zhao, J. (2026) · Neurocomputing · doi:10.1016/j.neucom.2026.133035 · Cited by 3
Wu, L., Liu, X., Liu, C., Wang, H., & Huang, S. (2026) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2026.3668933 · Cited by 4
“Owing to possessing good convergence and tracking performance, the finite-time or fixed-time adaptive control schemes [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55] have received considerable attentions.”
Self-citationAdaptive fuzzy fixed‐time tracking control of nonlinear systems with unmodeled dynamics
Ai, Z., Wang, H., & Shen, H. (2024) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3850 · Cited by 3
“In Reference 28, the dynamic signal is developed into a finite-time form for the first time on the basis of References 20 and 21.”
Self-citationMeng, Z., Ma, J., & Wang, H. (2024) · Asian Journal of Control · doi:10.1002/asjc.3436 · Cited by 3
Self-citationZhang, L., Zhang, H., Qian, C., & Hua, C. (2024) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2024.107206 · Cited by 3
Self-citationLi, C., Xia, J., Zhang, J., & Shen, H. (2024) · Nonlinear Dynamics · doi:10.1007/s11071-024-10618-7 · Cited by 3
“In [23], for a class of strictly feedback nonlinear systems with dynamics uncertainties, a new finite-time dynamic signal is introduced to control the dynamic disturbances and achieve finite-time tracking performance of the system.”
Zhang, Q., & Shao, X. (2025) · International Journal of Fuzzy Systems · doi:10.1007/s40815-024-01929-3 · Cited by 3
Wu, R., Liu, X.-P., Chen, T., Sun, L., & Wang, N. (2025) · Actuators · doi:10.3390/act14020056 · Cited by 3
“In recent years, the advancement of finite-time control has led to the proposal of adaptive methods for uncertain nonlinear systems, which represent a further extension of backstepping methods [27].”
Dong, Z., Lv, M., Da, X., & Zhang, Q. (2025) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7864 · Cited by 3
Jiang, T., Yan, Y., Yu, S., Li, T., & Zhao, Y. (2025) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7909 · Cited by 3
“In the existing literature, many excellent control methods have been proposed, such as neural network, [5] optimal control, [6] backstepping, [7] and sliding mode con-Abbreviations: ANA,anti-nuclearantibodies;APC,antigen-presentingcells;IRF,interferonregulatoryfactor.”
Ge, M. R., Wang, B., Guan, L., & Zhou, K. (2025) · Nonlinear Dynamics · doi:10.1007/s11071-025-11127-x · Cited by 3
“Despite advancements in finite-time control methods, the settling time remains dependent on initial conditions [37].”
Zhao, X., Gao, Y., Huang, H., Fan, Q., Chen, J., Deveci, M., & Ding, W. (2025) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2025.116407 · Cited by 3
Wang, X., Liang, X., Hu, S., & Xin, Q. (2025) · Actuators · doi:10.3390/act14050215 · Cited by 3
“In order to improve the trajectory tracking control accuracy, researchers have proposed numerous advanced control algorithms, such as PID control [1,2], sliding mode control [3,4], adaptive control [5,6], iterative learning control [7,8], fuzzy control [9,10], and neural network control [11,12].”
Ren, B., Wang, H., Wu, T., Quan, S., Lun, Y., & Wang, Y. (2025) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2025.107874 · Cited by 3
Self-citationLiu, X., Sun, J., Yan, Y., & Wang, S. (2025) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2024.3456851 · Cited by 3
“The pendulum system with dynamic disturbances from [35] is described as The parameters of the physical variables are M = 0 .”
Adaptive Fuzzy Approximate Optimal Consensus of Lagrangian Agents: An EXTRA-Based Smoothing Approach
Psillakis, H. E., & Oikonomidis, K. A. (2023) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2023.3276394 · Cited by 3
“For example, adaptive fuzzy controllers were developed in [26] within the fixed/finite tracking control framework [27], [28].”
MethodFault‐tolerant adaptive tracking control for spacecraft attitude with asymptotic convergence
Yin, Y., Ning, X., Wang, Z. X., & Xia, D. (2024) · Asian Journal of Control · doi:10.1002/asjc.3323 · Cited by 3
“However, apart from parametric uncertainties, the above adaptive control strategy is not capable of handling unstructured uncertainties (e.g., unknown dynamics, exogenous disturbance, measurement noise), which are primary encountered in practical problems [12–14].”
Wang, X., Liu, H., Zhang, L., Gao, Y., & Wu, Y. (2024) · IET Control Theory and Applications · doi:10.1049/cth2.12640 · Cited by 3
Cui, M., & Wu, Z. (2024) · IET Control Theory and Applications · doi:10.1049/cth2.12662 · Cited by 3
Shen, Q., Lin, W., Cao, L., & Zhao, M. (2024) · Asian Journal of Control · doi:10.1002/asjc.3457 · Cited by 3
“A decentralized output tracking control strategy was developed in [4–8], where the nonlinear unknown functions are estimated by using fuzzy logic systems (FLSs) or neural networks (NNs).”
Jin, L., Su, L., Lü, S., Wang, K., & Wang, J. (2024) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3886 · Cited by 3
Jiang, Y., & Su, Y. (2024) · International Journal of Systems Science · doi:10.1080/00207721.2024.2409878 · Cited by 3
“So as to reach the stability of the system within a finite time, scholars have proposed many related research results (Cheng et al., 2023; Li, Li, et al., 2023; H. Wang et al.,2023 ; H. Zhou et al., 2022; S. L. Zhu et al., 2022).”
Gao, D., Cui, W.-H., Wu, L., Zhang, Y., & Tao, Y. (2025) · Applied Mathematics and Computation · doi:10.1016/j.amc.2025.129628 · Cited by 3
Huang, J., Ye, Z., Ni, H., Zhang, D., & Abdulaal, M. J. (2024) · Transactions of the Institute of Measurement and Control · doi:10.1177/01423312241242840 · Cited by 2
“In Wang et al. (2023), a class of adaptive backstepping finite-time tracking control problem for feedback nonlinear systems with unmodeled dynamics and dynamic disturbances was studied.”
Adaptive Fuzzy Tracking Control and Its Application in Stochastic Biological Systems
Zhang, Y., Su, X., & Song, Y. (2024) · International Journal of Fuzzy Systems · doi:10.1007/s40815-024-01805-0 · Cited by 2
“For a class of nonlinear systems with unmodeled dynamics and dynamic perturbations, an adaptive backstepping finite-time tracking control strategy is proposed in [9].”
Bian, J., Zhang, Z., & Gao, Y. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7673 · Cited by 2
“For example [18], studied adaptive finite-time tracking control for a class of nonlinear systems with dynamic uncertainties, and [19] presented a fuzzy adaptive fixed-time feedback control algorithm for a class of nonlinear systems.”
High Performance Bounded Finite Time Control for Linear Systems With Input Saturation
Ma, W., & Liu, G. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7742 · Cited by 2
“An adaptive tracking control method was developed to achieve practically finite-time stability [24].”
Zhang, C., Zhou, M., Shao, X., & Zhang, X. (2025) · Control Engineering Practice · doi:10.1016/j.conengprac.2025.106528 · Cited by 2
Kharrat, M. (2025) · Transactions of the Institute of Measurement and Control · doi:10.1177/01423312251361970 · Cited by 2
“Command-filtered control methodologies have also incorporated fixed-time stability concepts to manage input quantization effects in practical implementations (Xu et al., 2022).”
Adaptive prescribed-time trajectory tracking control for USVs with disturbance and input saturation
Fan, Z., Wang, L., & Meng, H. (2025) · Nonlinear Dynamics · doi:10.1007/s11071-025-11841-6 · Cited by 2
Meng, Z., Wang, H., & Liu, X. (2025) · International Journal of Fuzzy Systems · doi:10.1007/s40815-025-02099-6 · Cited by 2
“Lemma 5 [36] : For the constants ψ ∈ R, (cid:17) ∈ R and c ≥ 1 , the following inequality satisfies Lemma 6 [37] : For ϒ ∈ R, (cid:19) ∈ R and τ ≥ 0 , the following inequality is described as in which m τ = 1 when τ < 1 , and m τ = 2 τ − 1 when τ ≥ 1 .”
Self-citationLiu, Y., Sun, Y., Hao, L., & Ma, H. (2025) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2025.108122 · Cited by 2
Bian, J., Mu, C., Xia, H., Si, C., Su, W., & Yi, J. (2026) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2026.3652650 · Cited by 2
“In this structure, the feedforward controller generally utilizes backstepping control to ensure tracking performance [21], [22].”
Metadata
- Authors
- Wang, H., Xu, K., & Zhang, H.
- Affiliations
- Bohai University (CN)
- Beijing Jiaotong University (CN)
- State Key Laboratory of Synthetical Automation for Process Industries (CN)
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2023-09
- Volume
- 68
- Issue
- 9
- Pages
- 5737-5744
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- 2334-3303
- OpenAlex
- W4312809224
- Cited by
- 342
- References
- 36
- Citations by year
- 2026: 69 · 2025: 108 · 2024: 111 · 2023: 54
- FWCI
- 27.48
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Automatic Control (publishedVersion)
- Funders
- National Natural Science Foundation of China (62173046, 51939001, 61976033)
- National Key R&D Program of China (2018YFA0702200)
- Fundamental Research Funds for the Central Universities (2022JBMC029)
- 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 › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Keywords
- finite-time tracking control, adaptive control, backstepping control, strict-feedback nonlinear systems, unmodeled dynamics, dynamic disturbances, finite-time stability, signal boundedness
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