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

• Published in: AIMS mathematics Vol. 9; no. 10; pp. 28447 - 28471
• Main Authors: Kong, Yihang, Zhang, Xinghui, Huang, Yaxin, Zhang, Ancai, Qiu, Jianlong
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: semi-global practical prescribed-time stable in probability; stochastic high-order nonlinear systems; unknown time-varying powers; unmodeled dynamics
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.20241380

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.