{"ID":2859952,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.04941","arxiv_id":"2510.04941","title":"A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation","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.","short_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...","url_abs":"https://arxiv.org/abs/2510.04941","url_pdf":"https://arxiv.org/pdf/2510.04941v2","authors":"[\"Adam Braun\",\"Lucas Brivadis\",\"Jean Auriol\"]","published":"2025-10-06T15:45:11Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}