Neural network-based adaptive finite-time tracking control for multiple inputs uncertain nonlinear systems with positive odd integer powers and unknown multiple faults

Miao Xiao; Zhe Lin; Qian Jiang; Dingcheng Yang; Xiongfeng Deng; Miao Xiao; Zhe Lin; Qian Jiang; Dingcheng Yang; Xiongfeng Deng

doi:10.3934/math.2025221

AIMS Mathematics

2025, Volume 10, Issue 3: 4819-4841. doi: 10.3934/math.2025221

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Neural network-based adaptive finite-time tracking control for multiple inputs uncertain nonlinear systems with positive odd integer powers and unknown multiple faults

1.
Zhejiang Dongfang Polytechnic, Wenzhou 325000, China
2.
Key Laboratory of Electric Drive and Control of Anhui Higher Education Institutes, Anhui Polytechnic University, Wuhu 241000, China

Received: 13 January 2025 Revised: 22 February 2025 Accepted: 26 February 2025 Published: 06 March 2025
MSC : 93A30, 93C10, 97N40

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.
- multiple-input nonlinear systems,
- finite-time control,
- unknown multiple faults,
- odd integer power,
- neural network
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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Abstract

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.

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