On the existence of KKL observers with nonlinear contracting dynamics (Long Version)

Victor Pachy (1) , Vincent Andrieu (2, 3) , Pauline Bernard (4) , Lucas Brivadis (5, 3) , Laurent Praly (4)

1 Mines Paris - PSL (École nationale supérieure des mines de Paris)
2 LAGEP - Laboratoire d'automatique et de génie des procédés
3 CFE - CNRS-formation Entreprise
4 CAS - Centre Automatique et Systèmes
5 L2S - Laboratoire des signaux et systèmes

KKL (Kazantzis-Kravaris/Luenberger) observers are based on the idea of immersing a given nonlinear system into a target system that is a linear stable filter of the measured output. In the present paper, we extend this theory by allowing this target system to be a nonlinear contracting filter of the output. We prove, under a differential observability condition, the existence of these new KKL observers. We motivate their introduction by showing numerically the possibility of combining convergence speed and robustness to noise, unlike what is known for linear filtering.

Domaines: Optimisation et contrôle [math.OC]

Victor Pachy, Vincent Andrieu, Pauline Bernard, Lucas Brivadis, Laurent Praly. On the existence of KKL observers with nonlinear contracting dynamics (Long Version). 2024. ⟨hal-04476312v2⟩