This paper presents a scheme for simultaneous fault estimation and fault-tolerant control of linear discrete time-varying stochastic systems. An observer is proposed to estimate the system state and the fault simultaneously. The estimation errors of both the system state and fault can achieve exponential stability in mean square sense even if the fault arbitrarily changes or is unbounded. The controllers of the drift term and diffusion term are designed separately, and then based on the estimated fault, the fault compensation is performed to realize fault tolerance. For the parameter design in the estimator and controllers, we provide two different algorithms via the cone complementarity linearization and the state transition matrix methods, respectively. As an extension, a class of quasi-linear systems is also discussed. A simulation example with two different fault types and an application in electromechanical servo systems are provided to illustrate the usefulness of the proposed scheme.

本文提出了一种用于线性离散时变随机系统的同时故障估计和容错控制的方案。提出了一个观测器来同时估计系统状态和故障。即使故障任意变化或无界，系统状态和故障的估计误差均能达到均方意义上的指数稳定性。分别设计漂移项和扩散项的控制器，然后根据估计的故障进行故障补偿，实现容错。对于估计器和控制器中的参数设计，我们分别通过锥互补线性化和状态转移矩阵方法提供了两种不同的算法。作为扩展，还讨论了一类拟线性系统。