存在多路数据丢失的线性离散时变系统故障检测滤波器设计

Fault Detection Filter Design for Linear Discrete Time-Varying Systems with Multiple Missing Measurements

本文研究一类存在多路测量数据丢失的线性离散时变系统故障检测滤波器设计问题,系统的数据丢失现象由一族在给定区间范围内取值的相互无关的随机变量描述。采用基于观测器的鲁棒H∞故障检测滤波器作为残差产生器,通过引入新的随机变量,将故障检测滤波器的设计问题转化为一类具有乘性噪声影响的随机时变系统有限时间域内的H∞滤波问题。运用Lyapunov函数法和伴随算子理论,基于Riccati方程推导并证明了使得滤波器增广系统满足均方指数稳定性和H∞性能的充分条件。将滤波器参数矩阵的求取转化为二次型优化问题,通过求解此Riccati方程,得到滤波器增益矩阵和后置滤波器矩阵的解析解。最后通过算例验证了所提算法的有效性。

This design problem of fault detection filter（FDF） for linear discrete time-varying systems with multiple missing measurements is dealt with.The uncertain observation phenomenon is depicted by a set of stochastic variables taking values on a certain interval and the variables are assumed to be unrelated with each other.By using an observer-based robust H∞-FDF as a residual generator,the design of FDF is formulated in the framework of H∞ filtering for a class of stochastic time-varying systems with multiplicative noises in finite-horizon.Based on Lyapunov function and adjoint operator methods,a sufficient condition to guarantee the mean square exponentially stability and H∞ performance of the derived augmented system is obtained in terms of a Riccati equation.The determination of the parameter matrices of the filter is converted into a quadratic optimization problem,and an analytical solution of the observer gain matrix and the post-filter matrix is given by solving the Riccati equation.The numerical example shows the effectiveness of the proposed method.