Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| hal.structure.identifier | Institut Montpelliérain Alexander Grothendieck [IMAG] | |
| dc.contributor.author | DE SAPORTA, Benoîte | |
| hal.structure.identifier | Instituto de Ciências Mathemàticas e de Computação [São Carlos] [ICMC-USP] | |
| dc.contributor.author | COSTA, Eduardo | |
| dc.date.accessioned | 2024-04-04T03:20:43Z | |
| dc.date.available | 2024-04-04T03:20:43Z | |
| dc.date.created | 2014-09-09 | |
| dc.date.issued | 2016 | |
| dc.identifier.issn | 0018-9286 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194610 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Ergodicité, contrôle et statistique pour les PDMP - ANR-12-JS01-0006 | |
| dc.language.iso | en | |
| dc.publisher | Institute of Electrical and Electronics Engineers | |
| dc.title.en | Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1109/TAC.2015.2495578 | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.identifier.arxiv | 1409.2631 | |
| bordeaux.journal | IEEE Transactions on Automatic Control | |
| bordeaux.page | 2035 - 2048 | |
| bordeaux.volume | 61 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 8 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01062618 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01062618v1 | |
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