DE SAPORTA, Benoîte; COSTA, Eduardo

doi:10.1109/TAC.2015.2495578

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Licence d’utilisation du document

DE SAPORTA, Benoîte
Quality control and dynamic reliability [CQFD]
Institut Montpelliérain Alexander Grothendieck [IMAG]

COSTA, Eduardo
Instituto de Ciências Mathemàticas e de Computação [São Carlos] [ICMC-USP]

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Article de revue

Ce document a été publié dans

IEEE Transactions on Automatic Control. 2016, vol. 61, n° 8, p. 2035 - 2048

Institute of Electrical and Electronics Engineers

Résumé en anglais

The aim of this paper is to propose a new numerical approximation of the Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is based on the selection of typical trajectories of the driving semi-Markov chain of the process by using an optimal quantization technique. The main advantage of this approach is that it makes pre-computations possible. We derive a Lipschitz property for the solution of the Riccati equation and a general result on the convergence of perturbed solutions of semi-Markov switching Riccati equations when the perturbation comes from the driving semi-Markov chain. Based on these results, we prove the convergence of our approximation scheme in a general infinite countable state space framework and derive an error bound in terms of the quantization error and time discretization step. We employ the proposed filter in a magnetic levitation example with markovian failures and compare its performance with both the Kalman-Bucy filter and the Markovian linear minimum mean squares estimator.< Réduire