The maneuvering problem for nonlinear systems under stochastic disturbances is investigated in this paper. Firstly, the maneuvering control objectives in their stochastic version are described in the sense of moment with tunable design parameters. Then, quartic Lyapunov functions of stabilizing errors are adopted to deal with the unknown covariance noise. Based on the adaptive law and the filter-gradient update law, an adaptive maneuvering controller is designed by the backstepping technique, which makes the closed-loop system is exponentially practically stable in mean square. Furthermore, both the path tracking error and the velocity assignment error converge to neighborhoods of zero, and the radius of these neighborhoods can be adjusted arbitrarily small by tuning independent parameters. Finally, to demonstrate the controller's effectiveness in handling unknown covariance and ensuring the practical stability of the closed-loop system, simulations of the mobile robot system in stochastic environments are conducted with various design parameters and covariance settings.

中文翻译：

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具有未知协方差噪声的随机非线性系统的纵控制


该文研究了随机扰动下非线性系统的纵问题。首先，用可调设计参数的矩量感来描述随机版本中的机动控制目标。然后，采用稳定误差的四次方 Lyapunov 函数处理未知协方差噪声;基于自适应定律和滤波器梯度更新定律，采用反步技术设计了自适应机动控制器，使闭环系统在均方上呈指数级实际稳定。此外，路径跟踪误差和速度分配误差都收敛到零邻域，并且这些邻域的半径可以通过调整独立参数来任意调整。最后，为了证明控制器在处理未知协方差和确保闭环系统的实际稳定性方面的有效性，使用各种设计参数和协方差设置对随机环境中的移动机器人系统进行了仿真。