A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation
Optimization and Control
2026-04-21 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2510.04941,
title = {A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation},
author = {Adam Braun and Lucas Brivadis and Jean Auriol},
journal= {arXiv preprint arXiv:2510.04941},
year = {2026}
}