Prescribed-time adaptive stabilization of high-order stochastic nonlinear systems with unmodeled dynamics and time-varying powers

Yihang Kong; Xinghui Zhang; Yaxin Huang; Ancai Zhang; Jianlong Qiu; Yihang Kong; Xinghui Zhang; Yaxin Huang; Ancai Zhang; Jianlong Qiu

doi:10.3934/math.20241380

AIMS Mathematics

2024, Volume 9, Issue 10: 28447-28471. doi: 10.3934/math.20241380

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Prescribed-time adaptive stabilization of high-order stochastic nonlinear systems with unmodeled dynamics and time-varying powers

1.
School of Automation and Electrical Engineering, Linyi University, Linyi, 276000, China
2.
School of Information Science and Engineering, Shandong Normal University, Jinan, 250014, China

Received: 26 July 2024 Revised: 13 September 2024 Accepted: 29 September 2024 Published: 08 October 2024
MSC : 93D05, 93E15

In this paper, the control problem of prescribed-time adaptive neural stabilization for a class of non-strict feedback stochastic high-order nonlinear systems with dynamic uncertainty and unknown time-varying powers is discussed. The parameter separation technique, dynamic surface control technique, and dynamic signals were used to eradicate the influences of unknown time-varying powers together with state and input unmodeled dynamics, and to mitigate the computational intricacy of the backstepping. In a non-strict feedback framework, the radial basis function neural networks (RBFNNs) and Young's inequality were deployed to reconstruct the continuous unknown nonlinear functions. Finally, by establishing a new criterion of stochastic prescribed-time stability and introducing a proper bounded control gain function, an adaptive neural prescribed-time state-feedback controller was designed, ensuring that all signals of the closed-loop system were semi-global practical prescribed-time stable in probability. A numerical example and a practical example successfully validated the productivity and superiority of the control scheme.
Citation: Yihang Kong, Xinghui Zhang, Yaxin Huang, Ancai Zhang, Jianlong Qiu. Prescribed-time adaptive stabilization of high-order stochastic nonlinear systems with unmodeled dynamics and time-varying powers[J]. AIMS Mathematics, 2024, 9(10): 28447-28471. doi: 10.3934/math.20241380

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Abstract

In this paper, the control problem of prescribed-time adaptive neural stabilization for a class of non-strict feedback stochastic high-order nonlinear systems with dynamic uncertainty and unknown time-varying powers is discussed. The parameter separation technique, dynamic surface control technique, and dynamic signals were used to eradicate the influences of unknown time-varying powers together with state and input unmodeled dynamics, and to mitigate the computational intricacy of the backstepping. In a non-strict feedback framework, the radial basis function neural networks (RBFNNs) and Young's inequality were deployed to reconstruct the continuous unknown nonlinear functions. Finally, by establishing a new criterion of stochastic prescribed-time stability and introducing a proper bounded control gain function, an adaptive neural prescribed-time state-feedback controller was designed, ensuring that all signals of the closed-loop system were semi-global practical prescribed-time stable in probability. A numerical example and a practical example successfully validated the productivity and superiority of the control scheme.

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