Pré-Publication, Document De Travail Année : 2025

A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation

Résumé

We propose an observer design for a cascaded system composed of an arbitrary nonlinear ordinary differential equation (ODE) with a 1D heat equation. The nonlinear output of the ODE imposes a boundary condition on one side of the heat equation, while the measured output is on the other side. The observer design combines an infinitedimensional Kazantzis-Kravaris/Luenberger (KKL) observer for the ODE with a backstepping observer for the heat equation. This construction is the first extension of the KKL methodology to infinite-dimensional systems. We establish the convergence of the observer under a differential observability condition on the ODE. The effectiveness of the proposed approach is illustrated in numerical simulations.

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Dates et versions

hal-05281266 , version 1 (04-10-2025)
hal-05281266 , version 2 (17-04-2026)

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Adam Braun, Lucas Brivadis, Jean Auriol. A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation. 2026. ⟨hal-05281266v2⟩
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