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Adaptive Fuzzy Practical Fixed-Time Tracking Control of Nonlinear Systems
Abstract
This article investigates an adaptive practical fixed-time control strategy for the output tracking control of a class of strict feedback nonlinear systems. By utilizing a backstepping algorithm, finite-time Lyapunov stable theory, and fuzzy logic control, a novel adaptive practical fixed-time controller is constructed. Fuzzy logic systems are introduced to approximate the unknown items of the system. Theoretical analysis proves that under the presented control strategy, the closed-loop system is practically fixed-time stable, and the tracking error converges to a small neighborhood of the origin within a fixed-time interval, in which the convergence time has no connection with the initial states of the system. In the meantime, all the signals of the closed-loop system are bounded. Finally, a numerical example is presented to indicate the feasibility and effectiveness of the proposed method.
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“The advent of fixed-time control methods offers a viable approach to address the issue of swift convergence without relying on knowledge of the initial states [41][42][43].”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [41]
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Adaptive Fuzzy Control of Nonlinear Systems With Predefined Time and Accuracy
Wang, Q., Cao, J., & Liu, H. (2022) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2022.3169852 · Cited by 313
“Consequently, it is essential and significant to investigate the control problem of system (6) to get a fascinating control performance, which has been investigated in [45] and [46]; however, only the fixed time stability was considered.”
BackgroundWang, H., Xu, K. W., & Qiu, J. (2021) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2021.3073024 · Cited by 284
“In [48], [49], two practical fixed-time control approaches were presented for nonlinear uncertain systems.”
BackgroundSelf-citationAdaptive Fixed-Time Stabilization for a Class of Uncertain Nonlinear Systems
Meng, Q., Ma, Q., & Shi, Y. (2023) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2023.3244151 · Cited by 195
“…the adaptive backstepping technique, fixed-time control of uncertain nonlinear systems has attracted much attention, such as systems with parameteric uncertainty [15], systems with unknown controldirection[16]and[17],systemscontaininginputsaturation[18], error-constrainedsystems[19],justtonameafew.”
MethodXie, S., Chen, Q., & Yang, Q. (2022) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2022.3223253 · Cited by 166
“Owing to this merit, scholars have applied fixed-time control to various nonlinear systems [12], [13], [14], [15], [16], [17], [18], [19], [20].”
BackgroundAdaptive Fuzzy Fast Finite-Time Dynamic Surface Tracking Control for Nonlinear Systems
Wang, H., Xu, K. W., Liu, P. X., & Qiao, J. (2021) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2021.3098830 · Cited by 160
Self-citationFixed-Time Adaptive Neural Network Control for Nonlinear Systems With Input Saturation
Sun, W., Diao, S., Su, S., & Sun, Z. (2021) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2021.3105664 · Cited by 136
“1) Unlike the case studied in [35]–[37], this study further considers the actuator saturation phenomenon that exists in most practical systems.”
BackgroundMethodAdaptive Neural Network Finite-Time Dynamic Surface Control for Nonlinear Systems
Li, K., & Li, Y. (2020) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2020.3027335 · Cited by 130
Event-driven NN adaptive fixed-time control for nonlinear systems with guaranteed performance
Song, X., Sun, P., Song, S., & Stojanović, V. (2022) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2022.04.003 · Cited by 123
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Zhang, J., Li, S., Ahn, C. K., & Xiang, Z. (2021) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2021.3066297 · Cited by 115
Adaptive Fuzzy Fixed-Time Decentralized Control for Stochastic Nonlinear Systems
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Event-Triggered Fuzzy Adaptive Fixed-Time Tracking Control for Nonlinear Systems
Hu, X., Li, Y.-X., & Hou, Z. (2022) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2020.3035779 · Cited by 101
“Therefore, in order to solve this problem, fixed-time control methods were proposed in [25]–[27].”
BackgroundMethodInfluentialZhang, M., Dong, S., Wu, Z., Chen, G., & Guan, X. (2022) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2022.3205176 · Cited by 99
Chen, G., & Dong, J. (2024) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2023.3342854 · Cited by 99
“Many control methods have emerged for nonlinear systems, such as adaptive control [1], [2], robust control [3], finite/fixed-time control [4], [5], [6], [7], [8], [9] The authors are with the College of Information Science and Engineering, the State Key Laboratory of Synthetical Automation for…”
Predefined-Time Approximation-Free Attitude Constraint Control of Rigid Spacecraft
Xie, S., Chen, Q., & He, X. (2022) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2022.3183550 · Cited by 96
Hu, X., Li, Y., Tong, S., & Hou, Z. (2021) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2021.3118835 · Cited by 93
“To this end, fixed-time control is proposed [24]–[27].”
BackgroundSong, S., Park, J. H., Zhang, B., & Song, X. (2021) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2021.3070700 · Cited by 90
Adaptive Fuzzy Fault Tolerant Control for Robot Manipulators With Fixed-Time Convergence
Van, M., Sun, Y., McIlvanna, S., Nguyen, M. N., Khyam, M. O., & Ceglarek, D. J. (2023) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2023.3247693 · Cited by 89
“• Compared to the conventional adaptive FLSs [40], [41], which do not provide a fixed-time convergence for the adaptive laws, a new fixed-time convergence for the adaptive law of FLS is proposed in this paper.”
InfluentialChen, M., Ying-sen, L., Wang, H., Peng, K., & Wu, L. (2022) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2022.3206507 · Cited by 86
“3) In [13] and [42], it is essential to make sure that the tracking signal yd and its derivatives y (k) d (k = 1, 2, .”
BackgroundSelf-citationDesign of Adaptive Fuzzy Fixed-Time HOSM Controller Subject to Asymmetric Output Constraints
Ma, L., Mei, K., Ding, S., & Pan, T. (2023) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2023.3241147 · Cited by 86
“, fuzzy control [1], [2], [3] and backstepping control [4], [5], [6]), sliding mode control (SMC) is well-acknowledged for its insensitivity to uncertainties and rapid response [7], [8], [9].”
BackgroundSong, S., Park, J. H., Zhang, B., & Song, X. (2020) · IEEE Transactions on Circuits & Systems II Express Briefs · doi:10.1109/tcsii.2020.3001314 · Cited by 85
“By integrating with fixed-time stability theory and backstepping control, the adaptive control problems were studied in [16]–[18].”
MethodResultWan, L., Cao, Y., Sun, Y., & Qin, H. (2022) · ISA Transactions · doi:10.1016/j.isatra.2022.04.013 · Cited by 83
Adaptive Practical Fixed-Time Tracking Control With Prescribed Boundary Constraints
Chen, M., Wang, H., & Liu, X. (2021) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2021.3051076 · Cited by 80
“For comparison, the scheme without the prescribed boundary constrains in [18] and our presented scheme are both implemented to the controlled system, the initial states are the same as in [18].”
MethodSelf-citationHou, H., Liu, Y., Lan, J., & Liu, L. (2022) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2022.3195609 · Cited by 79
“Lemma 3 (See [33]): For any positive constants ψ1, ψ2 and ψ3, any real variables x̄ and ȳ, one gets |x̄|1 |ȳ|2 ≤ ψ1 ψ1 + ψ2 ψ3|x̄| + ψ2 ψ1 + ψ2 ψ ψ1 ψ2 3 |ȳ|12 .”
A Complex-Valued Variant-Parameter Robust Zeroing Neural Network Model and its Applications
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“The fixed time convergence refers that the designed algorithm can calculate the approximate time required for problem solving in advance based on partial parameter information, which has been deeply studied in many fields [36], [37], [38], [39], [40].”
BackgroundWei, F., Zhang, L., Niu, B., & Zong, G. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7497 · Cited by 74
Huang, C., Zhang, X., Zhang, G., & Deng, Y. (2021) · Ocean Engineering · doi:10.1016/j.oceaneng.2021.109026 · Cited by 73
Fixed-Time Stabilization for a Class of Output-Constrained Nonlinear Systems
Mei, K., Ding, S., & Chen, C. (2022) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2022.3146011 · Cited by 73
“Following the idea, the further studies regarding fixed-time control issues have been conducted [33]–[37].”
BackgroundPractically Predefined-Time Adaptive Fuzzy Tracking Control for Nonlinear Stochastic Systems
Zhang, T., Su, S., Wei, W., & Yeh, R.-H. (2023) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2023.3272581 · Cited by 73
“Lemma 2 [22]: [13]: For any φ ∈ R and ϕ > 0, the following inequality: Lemma 4 [33]: (cid:2) [34]: Let constants φ > 0, ϕ > 0 and the function g ( x , y ) > 0.”
BackgroundMethodInfluentialPractical Finite-Time Command Filtered Backstepping With its Application to DC Motor Control Systems
Zheng, X., Yu, X., Jiang, J., & Yang, X. (2023) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2023.3269478 · Cited by 70
“To list a few, a novel adaptive fuzzy practical fixed-time controller was designed in [13] for a class of strict-feedback nonlinear systems by combining adaptive fuzzy backstepping technique with fixed-time Lyapunov stability.”
MethodYao, Y., Tan, J., Wu, J., & Zhang, X. (2021) · Nonlinear Dynamics · doi:10.1007/s11071-021-06633-7 · Cited by 69
Zhang, T., Bai, R., & Li, Y. (2022) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2022.3197970 · Cited by 68
“3: Compared with the existing finite-time control or fixed-time control results [33], [35], Lemma 3.”
BackgroundYou, S., Gil, J., & Kim, W. (2021) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2021.3123614 · Cited by 67
“Moreover, a neural network (NN) approximation-based control method has been proposed [27]– [30].”
MethodHuang, C., Xu, H., Batista, P., Zhang, X., & Soares, C. G. (2023) · European Journal of Control · doi:10.1016/j.ejcon.2023.100784 · Cited by 67
Fixed-Time Fractional-Order Sliding Mode Controller for Multimachine Power Systems
Huang, S., Xiong, L., Wang, J., Li, P., Wang, Z., & Ma, M. (2020) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2020.3043891 · Cited by 63
“Lemma 2: [37]–[38] The nonlinear system would converge to the equilibrium point within an upper bound time, if the system can satisfy the following condition,”
BackgroundAdaptive Neural Fixed-Time Control for Uncertain Nonlinear Systems
Liu, S., Wang, H., Li, T., & Xu, K. W. (2022) · IEEE Transactions on Circuits & Systems II Express Briefs · doi:10.1109/tcsii.2022.3146840 · Cited by 60
“Combining intelligent control technique, the fixed-time system control problem is discussed with unknown functions in [23], [24].”
MethodSelf-citationWang, J., Wang, C., Chen, C. L. P., Liu, Z., & Zhang, C. (2022) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2022.3225287 · Cited by 59
“Remark 1: Assumptions 1-2 are quite common, which is widely adopted in the design of control schemes for uncertain nonlinear systems, such as [4], [21], [27], and [34].”
BackgroundMachine Learning Methods for Intrusive Detection of Wormhole Attack in Mobile Ad Hoc Network (MANET)
Abdan, M., & Seno, S. A. H. (2022) · Wireless Communications and Mobile Computing · doi:10.1155/2022/2375702 · Cited by 57
Sun, W., Wu, J., Su, S., & Zhao, X. (2022) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2022.3201504 · Cited by 57
“Therefore, it is of great significance to design adaptive fixed-time control strategies for uncertain nonlinear systems; see for representative examples [16], [17], [18], [19], [20], [21], [22].”
BackgroundResultAdaptive fuzzy finite-time control of stochastic nonlinear systems with actuator faults
Wang, L., Wang, H., & Liu, P. X. (2021) · Nonlinear Dynamics · doi:10.1007/s11071-021-06309-2 · Cited by 56
Self-citationAdvancements, Challenges, and Future Trajectories in Advanced Battery Safety Detection
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Li, Y., Xu, N., Niu, B., Chang, Y., Zhao, J., & Zhao, X. (2021) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3283 · Cited by 51
“Based on formula (24), (23) can be rewritten in the following form: ?̇? = A0ξ + n ∑”
BackgroundJin, D., & Xiang, Z. (2024) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2024.3387441 · Cited by 51
“Lemma 2 [22]: For positive constants (cid:9) 1 , (cid:9) 2 , (cid:9) 3 and M ∈ R , m ∈ R , the following inequality holds: (5) Lemma 3 [26]: where λ min ( L + B ) denotes the minimum eigenvalue of L + B .”
BackgroundMethodInfluentialWang, J., Wang, C., Liu, Z., Chen, C. L. P., & Zhang, C. (2023) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2022.3211658 · Cited by 47
“The solution of the system can converge into the following residual set: Lemma 2 [36]: Lemma 3 [37]: For ∀ (cid:13) ∈ R and ∀ σ > 0, it is true that Lemma 4 [38]: Lemma 5 [38]: For x ∈ R , y ∈ R and any positive constants k 1 , k 2 , and m , it is true that Assumption 1 [22]: The desired output…”
BackgroundYu, Z., Li, Y., Lv, M., Chang, J., & Pei, B. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-022-07904-7 · Cited by 44
“Lemma 2.[32] For any given positive constants a1, a2, and a3, it holds that |x|1|y|2 6 a1 a1+a2 a3|x|+ a2 a1+a2 a − a1 a2 3 |x| a1+a2 .”
Xia, J., Wang, X., Park, J. H., Xie, X., & Chen, G. (2022) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2022.3172503 · Cited by 44
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Zhou, Z., Zhu, F., Xu, D., Chen, B., Guo, S., & Dai, Y. (2022) · IEEE Transactions on Intelligent Vehicles · doi:10.1109/tiv.2022.3215133 · Cited by 42
“j=1 κj ⎞ ⎠ a2 , 1 < a2 ≤ ∞ Lemma 5 ([30]): For κ ∈ R and ∀א > 0, it has 0 ≤ |κ| < א+ κ2/√κ2 + א2.”
Saturated Adaptive-Law-Based Backstepping and Its Applications to a Quadrotor Hover
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Jiang, H., Ma, Q., & Guo, J. C. (2023) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2023.3318572 · Cited by 40
“Although the fixed-time stability results [20], [21], [22] have decreased convergence time, the singularity problem is typically unavoidable in backstepping-based fixed-time controller design.”
BackgroundYu, Y., Zhang, Z., Zhong, M., & Wang, Z. (2021) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2021.11.036 · Cited by 39
Liu, W., Ma, Q., & Xu, S. (2023) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2023.3325529 · Cited by 38
“In [12], a novel adaptive practical fixed-time control scheme for a kind of nonlinear systems in strict-feedback form via output-feedback tracking regulation was constructed.”
BackgroundWu, Y., Zhang, G., & Wu, L. (2021) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2021.3065538 · Cited by 38
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“More complex approximation methods can be used to further reduce the error [33], [34], but it will increase the running cost of the model.”
MethodWang, C., Wang, J., Guo, Q., Liu, Z., & Chen, C. L. P. (2025) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2024.3429638 · Cited by 36
Kang, S., Liu, P. X., & Wang, H. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-022-07731-w · Cited by 36
“According to Lemmas 3 and 4 in [32], we have”
BackgroundSelf-citationWang, K., Liu, X., & Jing, Y. (2021) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2021.3083800 · Cited by 36
“In comparison with the existing results [43]–[45], the adopted control techniques are different.”
BackgroundMethodResultSelf-citationCommand filter-based adaptive fuzzy decentralized control for large-scale nonlinear systems
Kang, S., Liu, P. X., & Wang, H. (2021) · Nonlinear Dynamics · doi:10.1007/s11071-021-06779-4 · Cited by 36
Self-citationLv, J., Ju, X., & Wang, C. (2023) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2023.3296194 · Cited by 35
“Unfortunately, finite-time and fixed-time controllers [1], [2], [3], [4], [5], [6], [8], [9], [10], [11], [12], [13], [14] fail to do so.”
MethodNaderolasli, A., Shojaei, K., & Chatraei, A. (2023) · European Journal of Control · doi:10.1016/j.ejcon.2023.100903 · Cited by 34
Wang, C., Guo, Q., Wang, J., Liu, Z., & Chen, C. L. P. (2024) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2024.3371050 · Cited by 34
“For example, Chen et al. [16] investigated the fixed-time tracking control for strict-feedback nonlinear systems.”
BackgroundLai, G., Zhang, Y., Liu, Z., Wang, J., Chen, K., & Chen, C. L. P. (2021) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2021.3049902 · Cited by 34
Zhou, Y., Dong, W., Liu, Z., Lv, M., Zhang, W., & Chen, Y. (2022) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2022.3223121 · Cited by 33
“• To address the singularity issue that appears in the derivatives of fractional power terms by incorporating fixed-time control method under backstepping framework [25], [34], this article proposes a non-singular fixed-time tracking control method for UAV, which can keep the control variable to be finite when the tra…”
MethodZhang, J., Fu, Y., & Fu, J. (2023) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2023.3308573 · Cited by 33
Adaptive neural tracking control of high-order nonlinear systems with quantized input
Wang, H., Liu, S., Wang, D., Niu, B., & Chen, M. (2021) · Neurocomputing · doi:10.1016/j.neucom.2021.05.054 · Cited by 33
Self-citationLv, M., Li, Y., Wan, L., Dai, J., & Chang, J. (2022) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2022.3157393 · Cited by 33
“The peculiar feature of fixed-time stability consists in that convergence rate can be prescribed a priori via the so-called fixed-time tracking concept: appropriate modifications to standard design methodologies need to be made to achieve fixed-time tracking [21]–[24], [26].”
BackgroundNovel fast fixed-time sliding mode trajectory tracking control for manipulator
Zhang, X., & Shi, R. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.112469 · Cited by 31
Xie, H., Jing, Y., Zhang, J., & Dimirovski, G. M. (2024) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2024.3390440 · Cited by 30
“…1 − δ 2 ] / 2 ) [21], [27], [34]; 3) different from the practical finite-and fixed-time control schemes with unknown tracking accuracy [3], [4], [5], [6], [7], our approach fulfills trajectory tracking with the predefined settling time and accuracy; and 4) in comparison with the tuning function-based…”
BackgroundResultInfluentialZhu, Z., & Zhu, Q. (2022) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2022.3229073 · Cited by 30
“Lemma 4 (See [25]): For any k1 ∈ and k2 ∈ , the following inequality holds: 0 ≤ |k1| < k2 + k(2) 1(k(2) 1 + k(2) 2) 1 2 .”
Solving Time-Varying Nonsymmetric Algebraic Riccati Equations With Zeroing Neural Dynamics
Simos, T. E., Katsikis, V. N., Mourtas, S. D., & Stanimirović, P. S. (2023) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2023.3284533 · Cited by 29
“The tracking control has become one of the most important schemes in past studies [24], [25], [26], [27], [28].”
BackgroundMethodFixed-Time Neural Control of a Quadrotor UAV With Input and Attitude Constraints
Gao, B., Liu, Y., & Liu, L. (2023) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2023.123045 · Cited by 28
Chen, J., & He, C. (2021) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2021.3099470 · Cited by 27
Yang, J. L., Liu, B., Zhang, T., Hong, J., & Zhang, H. (2022) · Energy · doi:10.1016/j.energy.2022.125877 · Cited by 27
Fang, X., Fan, H., Liu, L., & Wang, B. Y. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-022-07784-x · Cited by 26
“An adaptive fuzzy fixed-time control strategy was proposed in [33] for a class of SISO nonlinear systems.”
MethodFan, Y., Shi, Y., Mu, D., Liu, J., & Li, Z. (2023) · Ocean Engineering · doi:10.1016/j.oceaneng.2023.115533 · Cited by 26
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
Self-citationZeng, D., Cai, C., Zhao, J., & Liu, Y. (2023) · Control Engineering Practice · doi:10.1016/j.conengprac.2023.105789 · Cited by 25
Fuzzy synchronization of fractional-order chaotic systems using finite-time command filter
Alassafi, M. O., Ha, S., Alsaadi, F. E., Ahmad, A. M., & Cao, J. (2021) · Information Sciences · doi:10.1016/j.ins.2021.08.005 · Cited by 25
Command filtered fixed‐time control for a class of multi‐agent systems with sensor faults
Dong, G., Li, X., Yao, D., Li, H., & Lu, R. (2021) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.5793 · Cited by 25
“Lemma 1 (See the work of Chen et al. 47 ).”
Yuan, F., Ma, Y., Liu, Y., Lan, J., & Xu, T. (2021) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2021.09.027 · Cited by 25
Position Control of a Mobile Robot through Deep Reinforcement Learning
Quiroga, F., Hermosilla, G., Farías, G., Fábregas, E., & Montenegro, G. (2022) · Applied Sciences · doi:10.3390/app12147194 · Cited by 29
“Additionally, different approaches are available, such as finite-time adaptive fault-tolerant control [8] and adaptive fuzzy control algorithms [9], which have been used for nonlinear systems in mobile robotics, as in [10].”
MethodWang, C., Wang, J., Du, Y., Zhang, C., Liu, Z., & Chen, C. L. P. (2023) · Information Sciences · doi:10.1016/j.ins.2023.03.010 · Cited by 25
Yao, Y., Tan, J., Yao, Y., Zhang, X., & Chen, P. (2023) · Neurocomputing · doi:10.1016/j.neucom.2023.127200 · Cited by 24
Non-singular terminal sliding mode cooperative guidance law under impact angle constraint
Dong, F., Zhang, X., & Tan, P. (2024) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2024.107079 · Cited by 24
Cuan, Z., & Ding, D. (2023) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2023.3292843 · Cited by 23
“6 reveals simulation results using the method in [26], which inferred that the tracking performance can not be assured and the control objective fails to be accomplished.”
MethodResultInfluentialLi, J., Wang, Q., & Fang, Y. (2024) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2024.108085 · Cited by 23
Adaptive fixed-time control for Lorenz systems
Wang, H., Yue, H., Liu, S., & Li, T. (2020) · Nonlinear Dynamics · doi:10.1007/s11071-020-06061-z · Cited by 23
Self-citationWu, Z., Guo, J., Liu, B., Ni, J., & Bu, X. (2021) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.5582 · Cited by 23
Adaptive fixed‐time tracking control for stochastic pure‐feedback nonlinear systems
Liang, Y., Li, Y., & Hou, Z. (2021) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3285 · Cited by 23
“s [?̇?(x(v)) + k1ξ(x(v)) + k2ξq(x(v)) − ρ]dv ≤ 0 (13) According to Lemma 1, for ∀t ≥ 0, we have ?̇?(x(t)) ≤ −k1ξ(x(t)) − k2ξ(x(t)) + ρ (14) Therefore, for ∀φ ∈ (0, 1), one has ?̇?(x(t)) ≤ − k1ξ(x(t)) − φk2ξ(x(t)) − (1 − φ)k2ξ(x(t)) + ρ (15) or ?̇?(x(t)) ≤ − φk1ξ(x(t)) − (1 − φ)k1ξ(x(t)) − k2ξ(x(t)) + ρ (16)”
Song, Z., & Sun, K. (2021) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2021.08.036 · Cited by 23
Wang, J., Wang, C., Zhang, C., Liu, Z., & Chen, C. L. P. (2023) · Fuzzy Sets and Systems · doi:10.1016/j.fss.2023.108563 · Cited by 23
An, S., Wang, X., Wang, L., & He, Y. (2023) · Ocean Engineering · doi:10.1016/j.oceaneng.2023.115158 · Cited by 23
Adaptive Approximation Tracking Control of a Continuum Robot With Uncertainty Disturbances
Xu, S., & He, B. (2022) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2022.3202540 · Cited by 22
“Considering the feed-back nonlinearity of systems, an adaptive fixed-time controller was proposed to achieve effective tracking [30].”
MethodYang, Y., Niu, Y., & Zhang, Z. (2020) · IET Control Theory and Applications · doi:10.1049/iet-cta.2020.0689 · Cited by 22
He, Z., Wang, G., & Fan, Y. (2023) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2023.07.043 · Cited by 21
Zhu, F., Zhao, Y., Fu, Y., & Dinh, T. N. (2023) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2023.3346442 · Cited by 21
“For example, the fuzzy logic system is taken to deal with nonlinear terms existing in the strict-feedback systems in [6], [7], [8], [9], where the controllers with adaptive parameters is constructed by backstepping scheme.”
Method
Metadata
- Authors
- Chen, M., Wang, H., & Liu, X.
- Affiliations
- University of Science and Technology Liaoning (CN)
- Bohai University (CN)
- Lakehead University (CA)
- Venue
- IEEE Transactions on Fuzzy Systems
- Published
- 2021-03
- Volume
- 29
- Issue
- 3
- Pages
- 664-673
- ISSN
- 1063-6706 (ISSN-L)
- 1941-0034
- OpenAlex
- W2995874545
- Cited by
- 405
- References
- 38
- Citations by year
- 2026: 35 · 2025: 77 · 2024: 65 · 2023: 86 · 2022: 65 · 2021: 66
- FWCI
- 19.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Fuzzy Systems (publishedVersion)
- Funders
- National Natural Science Foundation of China (61403177, 61773072)
- Natural Science Foundation of Liaoning Province (20180550319)
- Education Department Project of Liaoning Province of China (2019LNJC09)
- Taishan Scholar Project of Shandong Province of China (tsqn201812093)
- 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
- output tracking control, strict-feedback nonlinear systems, adaptive control, fuzzy systems, backstepping control, finite-time Lyapunov stability, signal boundedness
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