The paper presents a new Lyapunov-type predefined-time stabilization control algorithm for stochastic high-order nonlinear systems with asymmetric output constraints. In contrast to stochastic finite-time and fixed-time stabilization, the average value of the settling-time function for stochastic predefined-time stabilization control is independent of both the initial value and the control factors. To mitigate the significant uncertainties arising from the asymmetric output constraint, a tan-type barrier Lyapunov function is formulated. Furthermore, by harnessing the previously mentioned barrier Lyapunov function and integrating the power integrator technique, a controller design strategy is formulated based on the backstepping method. The rigorous analysis in this study proves that the designed controller ensures both the attainment of predefined-time convergence of the system states to the origin in probability and the satisfaction of the output constraint. Finally, an example of a roll angle subsystem for quadrotor UAVs and a numerical illustration are presented to corroborate the theoretical analysis.

中文翻译：

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随机非线性系统的预定义时间稳定及其在无人机上的应用

本文针对具有不对称输出约束的随机高阶非线性系统，提出了一种新的李亚普诺夫型预定义时间稳定控制算法。与随机有限时间和固定时间稳定相比，随机预定义时间稳定控制的稳定时间函数的平均值与初始值和控制因子无关。为了减轻由不对称输出约束引起的重大不确定性，制定了 tan 型势垒 Lyapunov 函数。此外，通过利用前面提到的势垒Lyapunov函数并集成功率积分器技术，基于反推法制定了控制器设计策略。本研究的严格分析证明，所设计的控制器既保证了系统状态在概率上达到预定时间收敛到原点，又保证了输出约束的满足。最后，提出了四旋翼无人机横滚角子系统的示例和数值说明来证实理论分析。