Filtering theory. With applications to fault detection, isolation, and estimation.
The present book contains a description of exact and almost input-decoupled filtering, \(H_2\) and \(H_\infty\) filtering and inverse filtering issues for linear processes. Moreover, applications of filtering and inverse filtering to fault detection, isolation and estimation are given. The book studies various classes of filtering problems and the corresponding filters to solve them. Various classes of filtering problems are defined based on different assumptions made on the noise characteristics and on different performance measures (indices) that are adapted. Each class of filtering problems is studied regarding i) the existence of a filter that solves it, ii) uniqueness of such a filter, and iii) designing such a filter while showing the flexibility in assigning poles of the filter. The book can be recommended to graduate students and researchers in filtering, signal processing and control. Prerequisites for the reader are a first graduate course in state-space methods as well as a first course in filtering. After an introduction and some preliminaries (list of symbols, list of acronyms, matrices, norms of deterministic and stochastic signals, norms of systems), in the third section a special coordinate basis for linear multivariable systems is given. The following sections are then: 4. Algebraic Riccati equations and matrix inequalities, 5. Exact disturbance decoupling via state and full information feedback, 6. Almost disturbance decoupling via state and full information feedback, 7. Exact input-decoupling filters, 8. Almost input-decoupled filtering under white noise input, 9. Almost input-decoupled filtering without statistical assumptions on input, 10. Optimally (sub optimally) input-decoupling filtering under white noise input -- \(H_2\) filtering, 11. Optimally (sub optimally) input-decoupled filtering without statistical information on the input -- \(H_\infty\) filtering, 12. Generalized \(H_2\) sub-optimally input-decoupled filtering, 13. Generalized \(H_\infty\) sub-optimally input-decoupled filtering, 14. Fault detection, isolation, and estimation -- exact or almost fault estimation, 15. Fault detection, isolation, and estimation -- optimal fault estimation.
scientific article; zbMATH DE number 5081230