Optimal residual generation for fault detection in linear discrete time-varying systems with uncertain observations |
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| Authors: | Yueyang Li Hamid Reza Karimi Choon Ki Ahn Yuan Xu Dong Zhao |
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| Institution: | 1. School of Electrical Engineering, University of Jinan, Jinan 250022, China;2. Department of Mechanical Engineering, Politecnico di Milano, Milan 20156, Italy;3. School of Electrical Engineering, Korea University, Seoul 136-701, Republic of Korea;4. Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Duisburg 47057, Germany |
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| Abstract: | This work deals with the problem of optimal residual generation for fault detection (FD) in linear discrete time-varying (LDTV) systems subject to uncertain observations. By introducing a generalized fault detection filter (FDF) with four parameter matrices as the residual generator, a novel FDF design scheme is formulated as two bi-objective optimization problems such that the sensitivity of residual to fault is enhanced and the robustness of residual to unknown input is simultaneously strengthened. A generalized operator based optimization approach is proposed to deduce solutions to the corresponding optimization problems in operator forms, where the related H∞/H∞ or FD performance index is maximized. With the aid of the addressed methods, the connections among the derived solutions are explicitly announced. The parameter matrices of the FDF are analytically derived via solving simple matrix equations recursively. It is revealed that our proposed results establish an operator-based framework of optimal residual generation for some kinds of linear discrete-time systems. Illustrative examples are given to show the applicability and effectiveness of the proposed methods. |
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| Keywords: | Corresponding author |
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