一类随机不确定线性系统集成故障检测与容错控制方法研究

本课题以一类随机不确定线性系统为研究对象，旨在研究其故障检测与容错控制的集成设计问题。首先对带乘性噪声的线性系统设计故障检测滤波器，定义基于广义传递函数算子的性能指标，将滤波器的设计归结为随机H∞/H∞或H－/ H∞最优化问题。提出基于Banach空间算子的最优化问题求解方法，通过解Riccati方程得到故障检测滤波器设计问题的最优解析解。在共用同一状态观测器的情况下，设计主动容错控制器，将故障检测滤波器和控制器的集成设计问题归纳为多目标优化问题，解决同时满足闭环控制系统设计要求和故障诊断系统性能指标的集成设计问题。其次，将上述结论推广到一类存在数据丢失的线性系统及一类具有随机时滞的线性系统，分别给出随机参数独立和参数依赖的故障检测滤波器与容错控制器集成设计方法。本项目的研究内容是故障诊断与容错控制领域尚未解决的前沿课题之一，具有重要的理论意义和现实意义。

This proposal aims to investigate the integrated design problem of fault detection and fault tolerant control for a class of stochastically uncertain linear systems. First, a fault detection filter will be designed for linear systems with multiplicative noise. By introducing generalized transfer funciton operaoter based performace indices, the fault detection filter design problem will be formulated into a stochastic H∞/H∞ or H－/ H∞ optimization framework. A new Banach space operater based method will be proposed for solving the aforementioned problem and the optimal analytical solution can be derived in terms of Riccati equation. In the case of active fault tolerant contoller and fault detection filter sharing a common observer, a multiple-objective optimization approach to integrated design fault dectetion filter and fault tolerant controller will be addressed such that closed-loop feedback control system performance and fault detection performance can achieve their optimal level simultaneously. Then, the proposed integrated design approach will be extended to a class of linear systems with missing measuments and a class of linear systems with random time-delay. Both stochastic parameter-independent and parameter-dependent methods for achieving integrated design of fault detection filter and fault tolerant controller will be derived. The main contents of this proposal belongs to one of the unsolved advanced topics in fault diagnosis and fault tolerant control area, which are of theoretical and practical significance.