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Set-membership state estimation and application on fault detection

Jun Xiong 1
1 LAAS-DISCO - Équipe DIagnostic, Supervision et COnduite
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : Modeling dynamic systems requires to account for uncertainties arising from noises impacting the measures and/or ! the dynamics, from lack of knowledge about disturbances, and also from uncertainties on parameter values (tolerance specifications, wear processes). Some of these uncertainties, like measurement noises, can be properly modelled in statistical terms but others are better characterized by bounds, without any additional feature. In this thesis, motivated by the above considerations, we consider the problem of integrating both statistical ans bounded uncertainties for discrete time linear systems. Building on the Interval Kalman Filter (IKF) developed by [Chen 1997], we propose significant improvements based on recent techniques of constraint propagation and set inversion which, unlike the IKF algorithm, allow us to obtain guaranteed results while controlling the pessimism of interval analysis. The improved filter is named iIKF. The iIKF filter has the same recursive structure as the classical Kalman filter and delivers an enclosure of all the possible optimal estimates and the covariance matrices. The previous IKF algorithm avoids the interval matrix inversion problem and consequently looses possible solutions. For the iIKF, we propose an original guaranteed method for the interval matrix inversion problem that couples the SIVIA (Set Inversion via Interval Analysis) algorithm and a set of constraint propagation problems. In addition, several mechanisms based on constraint propagation are implemented to limit the overestimation effect of interval propagation within the filter recursive structure. A fault detection algorithm based on the iIKF is proposed. It implements a semi-closed loop strategy which stops feeding the filter with observation corrupted by the fault as soon as it is detected. Through various examples, the advantages of the iIKF filter are presented and the effectiveness of the of the fault detection algorithm is demonstrated.
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  • HAL Id : tel-01068054, version 1

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Jun Xiong. Set-membership state estimation and application on fault detection. Automatique / Robotique. Institut National Polytechnique de Toulouse - INPT, 2013. Français. ⟨tel-01068054⟩

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