Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929572818190336 |
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| author | Alvarez, Hector Vargas Fabiani, Gianluca Kevrekidis, Ioannis G. Kazantzis, Nikolaos Siettos, Constantinos |
| author_facet | Alvarez, Hector Vargas Fabiani, Gianluca Kevrekidis, Ioannis G. Kazantzis, Nikolaos Siettos, Constantinos |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_12360 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks Alvarez, Hector Vargas Fabiani, Gianluca Kevrekidis, Ioannis G. Kazantzis, Nikolaos Siettos, Constantinos Numerical Analysis Artificial Intelligence Dynamical Systems 37N30, 68T05, 93C55, 65D15 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. |
| title | Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks |
| topic | Numerical Analysis Artificial Intelligence Dynamical Systems 37N30, 68T05, 93C55, 65D15 |
| url | https://arxiv.org/abs/2402.12360 |