Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks

• URL: http://arxiv.org/abs/2402.12360v1
• Date: Mon, 19 Feb 2024 18:47:56 GMT
• Title: Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks
• Authors: Hector Vargas Alvarez, Gianluca Fabiani, Ioannis G. Kevrekidis, Nikolaos Kazantzis, Constantinos Siettos
• Abstract summary: We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. The proposed PINN approach aims at learning a nonlinear state transformation map by solving a system of inhomogeneous functional equations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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