Tools for observers based on coordinate augmentation

Pauline Bernard (1) , Laurent Praly (1) , Vincent Andrieu (2)

1 CAS - Centre Automatique et Systèmes
2 LAGEP - Laboratoire d'automatique et de génie des procédés

Designing a non linear observer often requires to immerse the system dynamics into a space of greater dimension. In order to avoid the difficult left inversion of the immersion, coordinate augmentation has been proposed in [9]. However, difficulties in this augmentation via continuous Jacobian completion, losses of observability, or the question of completeness of solutions may arise in practice. This paper illustrates with the help of a toy-system how to overcome them by using tools and tricks such as extending the image of a diffeomorphism or adding fictitious outputs.

Mots clés: observers for non linear systems; coordinate augmentation; high gain observers; non linear Luenberger observers; Jacobian completion; diffeomorphism extension

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Pauline Bernard, Laurent Praly, Vincent Andrieu. Tools for observers based on coordinate augmentation. 2015 IEEE 54th Annual Conference on Decision and Control (CDC 2015), Dec 2015, Osaka, Japan. ⟨hal-01250483⟩