Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems
DE SAPORTA, Benoîte
Quality control and dynamic reliability [CQFD]
Institut Montpelliérain Alexander Grothendieck [IMAG]
Quality control and dynamic reliability [CQFD]
Institut Montpelliérain Alexander Grothendieck [IMAG]
DE SAPORTA, Benoîte
Quality control and dynamic reliability [CQFD]
Institut Montpelliérain Alexander Grothendieck [IMAG]
< Leer menos
Quality control and dynamic reliability [CQFD]
Institut Montpelliérain Alexander Grothendieck [IMAG]
Idioma
en
Article de revue
Este ítem está publicado en
IEEE Transactions on Automatic Control. 2016, vol. 61, n° 8, p. 2035 - 2048
Institute of Electrical and Electronics Engineers
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Proyecto ANR
Ergodicité, contrôle et statistique pour les PDMP - ANR-12-JS01-0006
Orígen
Importado de HalCentros de investigación