马尔可夫跳变系统的鲁棒故障检测与时域优化

Robust fault detection and time domain optimization for Markovian jump system

研究马尔可夫跳变系统(MJS)鲁棒故障检测滤波器(FDF)的设计与优化问题.基于观测器构建残差发生器,将相应的FDF设计问题转化为H∞滤波问题,以LMI的形式得到并证明了FDF存在的充分条件及求解方法.为进一步改善故障检测系统的性能,采用一种时域优化方法对其进行优化,并以矩阵Moore-Penrose逆的形式给出了该优化问题的最优解.数值仿真表明该方法具有较好的检测效果.

The problem of robust fault detection filter（FDF） design and optimization is studied for Markovian jump system （MJS）. An observer-based residual generator is constructed and the corresponding FDF design problem is formulated as an H∞ filtering problem. The solvable condition of the FDF and the solutions are obtained in terms of LMI. Furthermore, to improve the performance of the fault detection system, a time domain optimization approach is proposed. The solution of the optimization problem is given in the form of Moore-Penrose inverse of matrix. A numerical example is provided to show that the proposed approach has a good performance on detecting faults.