%0 Journal Article
%T 一类带有未知项的随机非完整系统的有限时间控制问题研究<br>Research on Finite-Time Control for a Class of Stochastic Nonholonomic Systems with Unknown Terms
%A 武茜茜
%J Pure Mathematics
%P 77-84
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.155155
%X 本文针对一类具有未知时变控制系数及随机噪声干扰的不确定项的随机非完整系统&#65292;研究其有限时间稳定问题。根据系统的特性&#65292;分两阶段进行控制设计&#65306;首先基于Lyapunov理论为<img src=\"https://html.hanspub.org/file/1252868-rId8.svg?20250519050741\" >子系统设计保证子系统稳定的控制输入<img src=\"https://html.hanspub.org/file/1252868-rId10.svg?20250519050741\" >&#65307;其次&#65292;通过对<img src=\"https://html.hanspub.org/file/1252868-rId12.svg?20250519050741\" >系统进行坐标变换转换成新形式<img src=\"https://html.hanspub.org/file/1252868-rId14.svg?20250519050741\" >系统&#65292;并采用递归反推法最终设计出全局控制输入<img src=\"https://html.hanspub.org/file/1252868-rId16.svg?20250519050741\" >。最终设计出全局控制输入理论分析表明&#65292;闭环系统的稳定性可通过随机Lyapunov函数<img src=\"https://html.hanspub.org/file/1252868-rId18.svg?20250519050741\" >的负定性严格证明&#65292;且系统状态在有限时间内收敛至平衡点。<br>This paper investigates the finite-time stabilization problem for a class of stochastic nonholonomic systems with unknown time-varying control coefficients and stochastic noise disturbances. Based on the system characteristics, a two-phase control design framework is proposed. First, a Lyapunov-based control input <img src=\"https://html.hanspub.org/file/1252868-rId20.svg?20250519050741\" > is designed for the <img src=\"https://html.hanspub.org/file/1252868-rId22.svg?20250519050741\" >-subsystem to ensure its stability. Subsequently, the original <img src=\"https://html.hanspub.org/file/1252868-rId24.svg?20250519050741\" >-system is transformed into a new structure <img src=\"https://html.hanspub.org/file/1252868-rId26.svg?20250519050741\" >-system via coordinate transformation, and a recursive backstepping approach is employed to synthesize the global control input <img src=\"https://html.hanspub.org/file/1252868-rId28.svg?20250519050741\" >. Theoretical analysis demonstrates that the closed-loop system&#8217;s stability can be rigorously proven through the negative definiteness of the stochastic Lyapunov function <img src=\"https://html.hanspub.org/file/1252868-rId30.svg?20250519050741\" >, ensuring probabilistic convergence of system states to the equilibrium point within a finite time. The proposed method effectively addresses uncertainties arising from time-varying control coefficients and stochastic disturbances, providing a systematic solution for finite-time stabilization of stochastic nonholonomic systems.
%K 随机非完整系统&#65292
%K 坐标变换&#65292
%K 有限时间稳定<br>Stochastic Nonholonomic System
%K Coordinate Transformation
%K Finite-Time Stabilization
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=114546