In this paper, some theoretical results of PID control of second order nonlinear uncertain stochastic system are given via inequalities. We extend the results of the corresponding deterministic systems to stochastic systems. Specifically, as long as we have a certain understanding of the upper bound of the derivative of the unknown nonlinear drift term and diffusion term, an analytic design method can be constructed for these three PID parameters to ensure the global stability and asymptotic stability of the closed-loop control systems. In addition, the numerical simulation results verify the theoretical analysis results.

中文翻译：

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用不等式技术分析一类不确定随机系统的控制

通过不等式给出了二阶非线性不确定随机系统PID控制的一些理论结果。我们将相应确定性系统的结果扩展到随机系统。具体而言，只要我们对未知的非线性漂移项和扩散项的导数的上限有一定的了解，就可以针对这三个PID参数构造解析设计方法，以确保闭环的全局稳定性和渐近稳定性。回路控制系统。另外，数值模拟结果验证了理论分析结果。