Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems

The application of autoencoders in combination with Dynamic Mode Decomposition for control (DMDc) and reduced order observer design as well as Kalman Filter design is discussed for low order state reconstruction of a class of scalar linear diffusion-convection-reaction systems. The general idea and...

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Autor principal:	Alexander Schaum
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	reduced order observers PDE models diffusion-convection-reaction systems dynamic mode decomposition autoencoders machine learning Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/278ae96426954533ba6013f88cae3a99
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spelling	oai:doaj.org-article:278ae96426954533ba6013f88cae3a992021-11-25T16:13:17ZAutoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems10.3390/a141103301999-4893https://doaj.org/article/278ae96426954533ba6013f88cae3a992021-11-01T00:00:00Zhttps://www.mdpi.com/1999-4893/14/11/330https://doaj.org/toc/1999-4893The application of autoencoders in combination with Dynamic Mode Decomposition for control (DMDc) and reduced order observer design as well as Kalman Filter design is discussed for low order state reconstruction of a class of scalar linear diffusion-convection-reaction systems. The general idea and conceptual approaches are developed following recent results on machine-learning based identification of the Koopman operator using autoencoders and DMDc for finite-dimensional discrete-time system identification. The resulting linear reduced order model is combined with a classical Kalman Filter for state reconstruction with minimum error covariance as well as a reduced order observer with very low computational and memory demands. The performance of the two schemes is evaluated and compared in terms of the approximated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mn>2</mn></msup></semantics></math></inline-formula> error norm in a numerical simulation study. It turns out, that for the evaluated case study the reduced-order scheme achieves comparable performance with significantly less computational load.Alexander SchaumMDPI AGarticlereduced order observersPDE modelsdiffusion-convection-reaction systemsdynamic mode decompositionautoencodersmachine learningIndustrial engineering. Management engineeringT55.4-60.8Electronic computers. Computer scienceQA75.5-76.95ENAlgorithms, Vol 14, Iss 330, p 330 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	reduced order observers PDE models diffusion-convection-reaction systems dynamic mode decomposition autoencoders machine learning Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
spellingShingle	reduced order observers PDE models diffusion-convection-reaction systems dynamic mode decomposition autoencoders machine learning Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95 Alexander Schaum Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems
description	The application of autoencoders in combination with Dynamic Mode Decomposition for control (DMDc) and reduced order observer design as well as Kalman Filter design is discussed for low order state reconstruction of a class of scalar linear diffusion-convection-reaction systems. The general idea and conceptual approaches are developed following recent results on machine-learning based identification of the Koopman operator using autoencoders and DMDc for finite-dimensional discrete-time system identification. The resulting linear reduced order model is combined with a classical Kalman Filter for state reconstruction with minimum error covariance as well as a reduced order observer with very low computational and memory demands. The performance of the two schemes is evaluated and compared in terms of the approximated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mn>2</mn></msup></semantics></math></inline-formula> error norm in a numerical simulation study. It turns out, that for the evaluated case study the reduced-order scheme achieves comparable performance with significantly less computational load.
format	article
author	Alexander Schaum
author_facet	Alexander Schaum
author_sort	Alexander Schaum
title	Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems
title_short	Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems
title_full	Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems
title_fullStr	Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems
title_full_unstemmed	Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems
title_sort	autoencoder-based reduced order observer design for a class of diffusion-convection-reaction systems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/278ae96426954533ba6013f88cae3a99
work_keys_str_mv	AT alexanderschaum autoencoderbasedreducedorderobserverdesignforaclassofdiffusionconvectionreactionsystems
_version_	1718413245589487616

Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems

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