The article discusses the adaptive fixed-time control problems for the stochastic pure-feedback nonlinear systems. Different from the existing results, the priori information of unknown virtual control coefficients (UVCC) is no longer needed in this article, which is realized by emplying the bound estimation method and well-defined smooth functions. A novel semi-global practical fixed-time stability criterion for the stochastic nonlinear systems is presented. Correspondingly, a new construction of Lyapunov function is proposed for the nonlinear stochastic system by adding the lower bounds of the UVCC. Based on the fuzzy logical system and fixed time stability theorem, a novel adaptive fuzzy fixed-time tracking control algorithm for stochastic nonlinear system is raised firstly. By theoretical analysis, we can conclude that the whole variables of the controlled system are bounded almost surely and the output can track the desired reference signal to a very small compact set within a predefined fixed-time interval. Finally, the raised method is illustrated by two simulation examples.

中文翻译：

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随机纯反馈非线性系统的自适应固定时间跟踪控制

本文讨论了随机纯反馈非线性系统的自适应固定时间控制问题。与现有结果不同，本文不再需要未知虚拟控制系数（UVCC）的先验信息，通过使用边界估计方法和定义良好的平滑函数来实现。提出了一种新的随机非线性系统的半全局实用固定时间稳定性判据。相应地，通过增加UVCC的下界，为非线性随机系统提出了一种新的Lyapunov函数构造。基于模糊逻辑系统和固定时间稳定性定理，首次提出了一种新的随机非线性系统自适应模糊固定时间跟踪控制算法。通过理论分析，我们可以得出结论，受控系统的整个变量几乎肯定是有界的，并且输出可以在预定义的固定时间间隔内将所需的参考信号跟踪到一个非常小的紧凑集。最后，通过两个仿真实例说明了提出的方法。