This article addresses the practically predefined-time adaptive fuzzy tracking control problem of strict-feedback nonlinear stochastic systems, where the system under consideration includes stochastic disturbances and uncertain parameters. First, in this study, practically predefined-time stochastic stabilization (PPSS) in the $p$ th moment sense is introduced, and a Lyapunov-type criterion for PPSS is proposed to assure the stabilization of the system considered. With these ideas, based on the backstepping design method, a semiglobally practically predefined-time adaptive fuzzy tracking control algorithm is proposed with a fuzzy system used to approximate the unknown part of the system. Moreover, the settling time of the system response can be arbitrarily adjusted in a mean-value sense, and such freedom can be used to improve the stochastic finite-/fixed-time control results. Finally, a practical example and a numerical example of a comparison are provided to validate the effectiveness of the proposed control strategy.

中文翻译：

---

非线性随机系统的实用预定义时间自适应模糊跟踪控制

本文解决了严格反馈非线性随机系统的实际预定义时间自适应模糊跟踪控制问题，其中所考虑的系统包含随机扰动和不确定参数。首先，在本研究中，实际上预定义时间随机稳定（PPSS） $p$ 引入了矩意义，并提出了 PPSS 的 Lyapunov 型准则，以确保所考虑系统的稳定性。基于这些思想，基于反步设计方法，提出了一种半全局实用预定义时间自适应模糊跟踪控制算法，用模糊系统来逼近系统的未知部分。此外，系统响应的稳定时间可以在平均值意义上任意调整，这种自由度可以用来改善随机有限/固定时间控制结果。最后，提供了一个实际例子和一个比较的数值例子来验证所提出的控制策略的有效性。