A closed-loop controlled system usually consists of the main structure, sensors, and actuators. The dynamics of sensors and actuators may influence the motion of the main structure. This article presents an analytical study on the first-passage reliability of a nonlinear stochastic controlled system under the consideration of the dynamics of sensors and actuators. The coupled dynamic equations of the controlled systems with sensors and actuators are first given, which are further integrated into a controlled, randomly excited, dissipated Hamiltonian system. By applying the stochastic averaging method for quasi-Hamiltonian systems, a one-dimensional averaged differential equation for the Hamiltonian function is obtained. The backward Kolmogorov equation associated with the averaged equation is then derived for the first-passage reliability analysis, from which the approximate reliability function and probability density of first-passage time are obtained. The accuracy of the proposed procedure is demonstrated by an example. A comparative analysis of the reliability of the system with/without sensors and actuators is carried out, which indicates that ignoring sensors and actuators will make underestimation of the reliability of the closed-loop system with small time. However, when time increases, there appears the opposite trend. Our findings provide a reference for control strategy design.

闭环控制系统通常由主要结构，传感器和执行器组成。传感器和执行器的动力学特性可能会影响主体结构的运动。本文提出了一种基于传感器和执行器动力学的非线性随机控制系统首次通过可靠性的分析研究。首先给出了带有传感器和执行器的受控系统的耦合动力学方程，将其进一步集成到受控的，随机激发的，耗散的哈密顿系统中。通过对准哈密顿系统采用随机平均方法，得到了哈密顿函数的一维平均微分方程。然后推导与平均方程关联的后向Kolmogorov方程，以进行首次通过可靠性分析，从中获得近似可靠性函数和首次通过时间的概率密度。实例证明了所提出程序的准确性。对带有/不带有传感器和执行器的系统的可靠性进行了比较分析，这表明忽略传感器和执行器会在短时间内低估闭环系统的可靠性。但是，随着时间的增加，出现相反的趋势。我们的发现为控制策略设计提供了参考。这表明忽略传感器和执行器会在短时间内低估闭环系统的可靠性。但是，随着时间的增加，出现相反的趋势。我们的发现为控制策略设计提供了参考。这表明忽略传感器和执行器会在短时间内低估闭环系统的可靠性。但是，随着时间的增加，出现相反的趋势。我们的发现为控制策略设计提供了参考。