This paper addresses the mean-square finite-time bounded control problem for uncertain stochastic systems via a sliding mode approach. The stochastic phenomena of randomly occurring uncertainties and randomly varying actuator faults modeled by two independent exponential distributions are addressed effectively. A key issue for the system under the consideration is how to ensure, for any prescribed finite (possibly short) working time interval, the stochastic finite-time boundedness (SFTB) of the resultant closed-loop systems and the reachability of the specified sliding surface in mean-square sense. To this end, a parameter-dependent sliding mode control (SMC) law is designed to force (with probability one) the state trajectories into a domain around the specified sliding surface during the given finite-time interval. The upper bound of the sliding domain associated with the design parameters is obtained explicitly. The sufficient conditions are established, respectively, for guaranteeing the SFTB of the SMC systems over both reaching phase and sliding motion phase. Finally, the proposed finite-time SMC approach is illustrated via a parallel active suspension system.

中文翻译：

---

具有随机变化执行器故障的不确定随机系统的有限时间有界控制的参数相关滑模方法及其在并联主动悬架系统中的应用

本文通过滑模方法解决了不确定随机系统的均方有限时间有界控制问题。有效地解决了由两个独立指数分布建模的随机发生的不确定性和随机变化的执行器故障的随机现象。所考虑系统的一个关键问题是如何确保对于任何规定的有限（可能很短）工作时间间隔，合成闭环系统的随机有限时间有界 (SFTB) 和指定滑动面的可达性在均方意义上。为此，设计了一种参数相关的滑模控制 (SMC) 定律，以在给定的有限时间间隔内将状态轨迹（以概率为 1）强制进入指定滑动表面周围的域中。与设计参数相关的滑动域的上限是明确获得的。分别建立了保证SMC系统在到达阶段和滑动阶段的SFTB的充分条件。最后，通过并联主动悬架系统说明了所提出的有限时间 SMC 方法。