Abstract

We use physics-informed neural networks (PINNs) to numerically solve the discrete-time nonlinear observer-based state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a nonlinear state transformation operator by solving a system of functional equations. The performance of the proposed approach is assessed via two illustrative case studies, for which the observer linearizing transformation operator can be derived analytically. We also perform an uncertainty quantification analysis for the proposed scheme. The performance and numerical approximation accuracy of the proposed scheme is compared with conventional power-series numerical implementation.

Recommended citation: Alvarez, H. V., Fabiani, G., Kevrekidis, I. G., Kazantzis, N., & Siettos, C. (2024). Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks. Chaos Solitons & Fractals 186. https://doi.org/10.1016/j.chaos.2024.115215