Dual parametric and state estimation for partial differential equations
Abstract
Designing estimation algorithms for systems governed by partial differential equations (PDEs) such as fluid flows is challenging due to the high-dimensional and oftentimes nonlinear nature of the dynamics, as well as their dependence on unobserved physical parameters. In this paper, we propose two different lightweight and effective methodologies for real-time state estimation of PDEs in the presence of parametric uncertainties. Both approaches combine a Kalman filter with a data-driven polytopic linear reduced-order model obtained by dynamic mode decomposition (DMD). Using examples involving the nonlinear Burgers and Navier-Stokes equations, we demonstrate accurate estimation of both the state and the unknown physical parameter along system trajectories corresponding to various physical parameter values.
Cite
@article{arxiv.2312.11839,
title = {Dual parametric and state estimation for partial differential equations},
author = {Saviz Mowlavi and Mouhacine Benosman},
journal= {arXiv preprint arXiv:2312.11839},
year = {2023}
}
Comments
Presented at IEEE CDC 2023. arXiv admin note: text overlap with arXiv:2302.01189