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

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.

Domains

Optimization and Control [math.OC]

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Micnon.pdf (469.94 Ko)

error_x_conv.pdf (33.74 Ko)

error_x_noise.pdf (41.79 Ko)

error_z_conv.pdf (33.11 Ko)

error_z_noise.pdf (42.86 Ko)

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https://hal.science/hal-04476312

Submitted on : Friday, March 15, 2024-9:33:48 AM

Last modification on : Friday, April 19, 2024-4:18:56 PM

Dates and versions

hal-04476312 , version 1 (24-02-2024)

hal-04476312 , version 2 (15-03-2024)

Identifiers

HAL Id : hal-04476312 , version 2
ARXIV : 2402.16432

Cite

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⟩

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