Linear Discrete Time Varying Systems H_ ¡Þ Fault Estimation Problem

With the development of the modern science and technology, industrial facilities are becoming large-scale, integrated, high-speed, automatic and intelligent. Once a failure happens in such a system, huge loss of lives and properties are usually unavoidable. In order to guarantee the safety and reliability of the control systems, researches on fault diagnosis have been more and more important. On the other hand, most of practical systems are time varying. However, few attentions have been paid to fault estimation of time-varying systems yet. In this thesis, problems related to H_∞ fault estimation for linear discrete time-varying systems are investigated in the framework of H_∞ filtering by applying Krein space Kalman filtering theory and innovation reorganized approach.Based on analyzing the background and significance of the research topic, brief reviewing of current development of fault diagnosis, and an introduction to innovation reorganization-based H_∞ filtering, multi-step prediction and multi-step smoothing in Krein space for linear time-varying systems, the main problems and organization of this thesis are stated firstly.Firstly, the problem of H_∞ fault estimation for linear discrete time-varying systems is studied by using the Krein space Kalman filtering theory and an innovation reorganized approach. Sufficient and necessary condition on the existence of H_∞ fault estimator is provided in terms of matrix Riccati equation and a steady state solution to the H_∞ fault estimation problem is also given. Secondly, a reduced-order ordinary linear discrete time-varying systems is presented to describe the dynamic behavior of a kind of singular time-varying systems and, based on this, the problem of H_∞ fault estimation for such kind of systems can be dealt with applying Krein space Kalman filtering. Thirdly, the problem of robust H_∞ fault estimation for linear discrete time-varying systems with model uncertainty is considered. With the aid of state augment, the problem of robust H_∞ fault estimation for the uncertain linear discrete time-varying systems can be formulated as H_∞ fix-lag smoothing and solved by using Krein space Kalman filtering theory and innovation reorganized approach. Furthermore, the problem of H_∞ fault estimation for linear discrete time-varying systems with delayed measurements is also studied. Using Krein space white noise filtering theory and the innovation reorganized approach, the problem of H_∞ white noise estimation for such kind of time-delay systems is solved and the obtained results can be further applied to the H_∞ fault estimation.Finally, both a short conclusion of this thesis and future research topics in this field are given.