Optimal fault detection for linear discrete time-varying systems

• Published in: Automatica (Oxford) Vol. 46; no. 8; pp. 1395 - 1400
• Main Authors: Zhong, Maiying, Ding, Steven X., Ding, Eve L.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2010; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Design engineering; Exact sciences and technology; Fault detection; Linear discrete time-varying system; Mathematical analysis; Mathematical models; Modelling and identification; Noise; Observer; Optimization; Post-filter; Riccati equation; Stochasticity; Post-filter; Linear discrete time-varying system; Fault detection; Riccati equation; Observer; Unknown input; Probabilistic approach; L2 approximation; Optimal detection; Optimization; Finite horizon; Filter; Discrete time; System identification; Fault diagnostic; Defect detection
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2010.05.022

This paper deals with the problem of observer-based fault detection for linear discrete time-varying (LDTV) systems. A problem formulation is first proposed to address the optimization of the fault detection filter (FDF) design, which is expressed in terms of maximizing a finite horizon H ∞ / H ∞ or H − / H ∞ performance index. This formulation can be applied to FDF design of LDTV systems subject to l 2 -norm bounded unknown inputs or stochastic noise sequences. It is shown that a unified optimal solution to the FDF can be obtained by solving the discrete time Riccati equation and the optimal FDF is not unique. A numerical example is given to illustrate the proposed method.