具有多测量数据包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 Packet Dropouts

研究存在多数据包丢失现象的线性离散时变系统有限时间域内故障检测滤波器(Fault detection filter,FDF)设计问题.在数据包具有时间戳标记的条件下,设计基于观测器的FDF作为残差产生器,构造两类FDF.其一为H-/H∞-FDF或H∞/H∞-FDF.定义故障到残差和未知输入到残差的广义传递函数算子,将此类FDF设计问题转换为随机意义下H-/H∞或H∞/H∞性能指标优化问题.其二为H∞-FDF,将此类FDF设计问题转化为随机意义下的H∞滤波问题.采用基于伴随算子的H∞优化方法,通过求解递推Riccati方程,得到上述两类FDF设计问题的解析解.通过算例验证所提方法的有效性.

This paper is concerned with the fault detection filter（FDF） design problem for linear discrete time-varying（LDTV） systems with multiple data packet dropouts in finite-horizon. Under the condition that the data packet is time-stamped, a conventional observer-based FDF is proposed as a residual generator. Two categories of the FDFs are constructed. One is H-/H∞-FDF or H∞/H∞-FDF. By defining generalized transfer function operators that map fault/unknown input to residual, the FDF design problem is formulated in the framework of optimizing H-/H∞or H∞/H∞performance index in a stochastic sense. The other one is the H∞-FDF, and the FDF design issue is formulated in the framework of H∞filtering. By employing the adjoint-based optimization approach, analytical solutions to the aforementioned FDF design problems are derived via solving recursive Riccati equations. Numerical examples are given to show the effectiveness of the addressed method.