Practical finite-time adaptive neural network control for fractional-order nonlinear systems

Ting Kang; Wenyang Yang; Boqiang Cao; Ting Kang; Wenyang Yang; Boqiang Cao

doi:10.3934/era.2026362

Electronic Research Archive

2026, Volume 34, Issue 11: 8569-8590. doi: 10.3934/era.2026362

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Practical finite-time adaptive neural network control for fractional-order nonlinear systems

1.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
2.
Ningxia Basic Science Research Center of Mathematics, Yinchuan 750021, China
3.
Ningxia Key Laboratory of Interdisciplinary Mechanics and Scientific Computing, Yinchuan 750021, China

Received: 26 July 2026 Revised: 14 September 2026 Accepted: 21 September 2026 Published: 08 October 2026

This paper investigates the semi-global practical finite-time adaptive neural network (NN) control problem for a class of fractional-order nonlinear systems with unknown nonlinearities. First, a novel practical finite-time stability criterion is established for fractional-order nonlinear systems. In contrast to analyses based on specific derivative properties of composite Lyapunov functions, the proposed criterion is rigorously developed through direct estimation of the fractional-order derivative of the Lyapunov function. This direct estimation framework provides a general stability analysis approach with independently adjustable convergence and residual-set parameters, thereby enhancing the flexibility of controller design. Second, an adaptive NN controller is developed based on this criterion, where NNs are employed to approximate the unknown nonlinearities. It is proven that the proposed control scheme ensures semi-global practical finite-time stability of the closed-loop system and boundedness of all closed-loop signals. Finally, numerical simulation results are provided to demonstrate the effectiveness of the proposed control scheme.
- fractional-order nonlinear systems,
- practical finite-time stability,
- adaptive neural network control,
- Lyapunov method
Citation: Ting Kang, Wenyang Yang, Boqiang Cao. Practical finite-time adaptive neural network control for fractional-order nonlinear systems[J]. Electronic Research Archive, 2026, 34(11): 8569-8590. doi: 10.3934/era.2026362

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Abstract

This paper investigates the semi-global practical finite-time adaptive neural network (NN) control problem for a class of fractional-order nonlinear systems with unknown nonlinearities. First, a novel practical finite-time stability criterion is established for fractional-order nonlinear systems. In contrast to analyses based on specific derivative properties of composite Lyapunov functions, the proposed criterion is rigorously developed through direct estimation of the fractional-order derivative of the Lyapunov function. This direct estimation framework provides a general stability analysis approach with independently adjustable convergence and residual-set parameters, thereby enhancing the flexibility of controller design. Second, an adaptive NN controller is developed based on this criterion, where NNs are employed to approximate the unknown nonlinearities. It is proven that the proposed control scheme ensures semi-global practical finite-time stability of the closed-loop system and boundedness of all closed-loop signals. Finally, numerical simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

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