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

2024/02/26 by Victor Pachy, Vincent Andrieu, Pachy, Victor +7 · 2 citations
Engineering · #Advanced Control Systems Optimization #Control and Stability of Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2402.16432

openalex created_date 2024/02/26 · openalex publication_date 2024/02/26 · openalex updated_date 2026/07/28

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.

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