Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks

TL;DR

This paper introduces a novel approach using Physics-Informed Neural Networks to solve nonlinear discrete-time observer problems, integrating exact linearization within a single-step framework and validating through case studies and uncertainty analysis.

Contribution

The paper presents a new PINN-based method for nonlinear observer linearization in discrete-time systems, combining functional equations with uncertainty quantification.

Findings

PINN approach successfully linearizes nonlinear observers in case studies.

Compared with power-series methods, PINNs provide accurate solutions with uncertainty estimates.

The method demonstrates potential for robust nonlinear state estimation.

Abstract

We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a nonlinear state transformation map by solving a system of inhomogeneous functional equations. The performance of the proposed PINN approach is assessed via two illustrative case studies for which the observer linearizing transformation map can be derived analytically. We also perform an uncertainty quantification analysis for the proposed PINN scheme and we compare it with conventional power-series numerical implementations, which rely on the computation of a power series solution.