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

TL;DR

This paper extends KKL observers by introducing nonlinear contracting filters, demonstrating their existence under certain conditions, and showing they can improve convergence speed and noise robustness in nonlinear system state estimation.

Contribution

The paper introduces a novel class of KKL observers with nonlinear contracting dynamics, expanding the theoretical framework and practical capabilities of nonlinear state observers.

Findings

Existence of nonlinear contracting KKL observers proven under differential observability.

Numerical evidence shows improved convergence speed and noise robustness.

Potential for better nonlinear system state estimation methods.

Abstract

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.