@article{Kong2024, 
author = {Yihang Kong and Xinghui Zhang and Yaxin Huang and Ancai Zhang and Jianlong Qiu},
title = {Prescribed-time adaptive stabilization of high-order stochastic nonlinear systems with unmodeled dynamics and time-varying powers},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {28447-28471},
keywords = {stochastic high-order nonlinear systems, semi-global practical prescribed-time stable in probability, unmodeled dynamics, unknown time-varying powers},
url = {https://www.sciopen.com/article/10.3934/math.20241380},
doi = {10.3934/math.20241380},
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.}
}