Accéder directement au contenu Accéder directement à la navigation
Pré-publication, Document de travail

NONLINEAR OBSERVER IN THE ORIGINAL COORDINATES WITH DIFFEOMORPHISM EXTENSION AND JACOBIAN COMPLETION

Abstract : Typical difficulties we face in implementing observers in applications are: – because of physical constraints or observability singularities, the estimated state should remain in some restricted region of the system state manifold ; – observability may also impose the observer dynamics to live in an observer state manifold with higher dimension than the system state. In such a case, the observer implementation needs a left inverse of an injective immersion. In the approach we propose to round these difficulties, we do not modify the given converging dynamics of the observer, assumed to be globally defined. Instead we select carefully the coordinates to express them. This is done via appropriate diffeomorphisms: – one diffeomorphism sending the restricted region to the whole space. This is done by an image extension. – one function extending the injective immersion into a diffeomorphism and making the observer state coordinates equivalent to the system state coordinates complemented with extra ones introduced to fill the dimension gap. This is done via a Jacobian completion. Such a design makes possible the expression of the observer dynamics in the, maybe complemented, original coordinates. Several examples illustrate our results.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01199791
Contributeur : Pauline Bernard <>
Soumis le : mercredi 16 septembre 2015 - 10:57:54
Dernière modification le : jeudi 9 avril 2020 - 17:08:12
Document(s) archivé(s) le : mardi 29 décembre 2015 - 07:27:58

Fichiers

ObsOriginalCoordinates_Final.p...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01199791, version 1
  • ARXIV : 1509.04865

Citation

Pauline Bernard, Vincent Andrieu, Laurent Praly. NONLINEAR OBSERVER IN THE ORIGINAL COORDINATES WITH DIFFEOMORPHISM EXTENSION AND JACOBIAN COMPLETION. 2015. ⟨hal-01199791v1⟩

Partager

Métriques

Consultations de la notice

106

Téléchargements de fichiers

81