This paper addresses the adaptive finite-time tracking control (FTTC) problem for multiple-input nonlinear systems (NSs). The system under consideration encompasses high-order nonlinear terms with positive odd integer powers, uncertain dynamics, parametric nonlinear dynamics, multiple unknown faults, and unknown control gains. The proposed adaptive FTTC strategy integrates the neural network (NN) approximation technique with the backstepping control approach. By employing the NN approximator, the challenge of approximating uncertain nonlinear dynamics and unknown nonlinear functions was effectively resolved. Concurrently, adaptive control laws for unknown parameters were formulated using the adaptive estimation method. Furthermore, to address unknown control coefficients arising from unknown faults and unknown control gains within the system, the Nussbaum gain function (NGF) was incorporated into the control design process. Subsequently, NN-based adaptive FTTC strategies were developed for inputs under various fault conditions. The designed control strategies ensured that all signals of the closed-loop system (ASCLS) with multiple faults maintain semi-global practical finite-time stability (SGPFS), and the tracking error of the system converges to a small neighborhood of zero within a finite time (SNZFT). Finally, the efficacy of the developed control method was validated through a simulation example.
Citation: Miao Xiao, Zhe Lin, Qian Jiang, Dingcheng Yang, Xiongfeng Deng. Neural network-based adaptive finite-time tracking control for multiple inputs uncertain nonlinear systems with positive odd integer powers and unknown multiple faults[J]. AIMS Mathematics, 2025, 10(3): 4819-4841. doi: 10.3934/math.2025221
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This paper addresses the adaptive finite-time tracking control (FTTC) problem for multiple-input nonlinear systems (NSs). The system under consideration encompasses high-order nonlinear terms with positive odd integer powers, uncertain dynamics, parametric nonlinear dynamics, multiple unknown faults, and unknown control gains. The proposed adaptive FTTC strategy integrates the neural network (NN) approximation technique with the backstepping control approach. By employing the NN approximator, the challenge of approximating uncertain nonlinear dynamics and unknown nonlinear functions was effectively resolved. Concurrently, adaptive control laws for unknown parameters were formulated using the adaptive estimation method. Furthermore, to address unknown control coefficients arising from unknown faults and unknown control gains within the system, the Nussbaum gain function (NGF) was incorporated into the control design process. Subsequently, NN-based adaptive FTTC strategies were developed for inputs under various fault conditions. The designed control strategies ensured that all signals of the closed-loop system (ASCLS) with multiple faults maintain semi-global practical finite-time stability (SGPFS), and the tracking error of the system converges to a small neighborhood of zero within a finite time (SNZFT). Finally, the efficacy of the developed control method was validated through a simulation example.
Monotonicity and inequalities related to complete elliptic integrals of the second kind
by Fei Wang, Bai-Ni Guo and Feng Qi. AIMS Mathematics, 2020, 5(3): 2732–2742.
DOI: 10.3934/math.2020176
In Acknowledgments section, the Grant number of "Project for Combination of Education and Research Training at Zhejiang Institute of Mechanical and Electrical Engineering" is missing. Here we give the complete information of this fund.
The changes have no material impact on the conclusion of this article. The original manuscript will be updated [1]. We apologize for any inconvenience caused to our readers by this change.
This work was partially supported by the Foundation of the Department of Education of Zhejiang Province (Grant No. Y201635387), the National Natural Science Foundation of China (Grant No. 11171307), the Visiting Scholar Foundation of Zhejiang Higher Education (Grant No. FX2018093), and the Project for Combination of Education and Research Training at Zhejiang Institute of Mechanical and Electrical Engineering (Grant No. A027120206).
The authors thank anonymous referees for their careful corrections to, helpful suggestions to, and valuable comments on the original version of this manuscript.
The authors declare that they have no conflict of interest.
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Miao Xiao, Zhe Lin, Qian Jiang, Dingcheng Yang, Xiongfeng Deng. Neural network-based adaptive finite-time tracking control for multiple inputs uncertain nonlinear systems with positive odd integer powers and unknown multiple faults[J]. AIMS Mathematics, 2025, 10(3): 4819-4841. doi: 10.3934/math.2025221
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