An Algebraic Approach to Identifiability

This paper addresses the problem of identifiability of nonlinear polynomial state-space systems. Such systems have already been studied via the input-output equations, a description that, in general, requires differential algebra. The authors use a different algebraic approach, which is based on dis...

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Main Authors:	Daniel Gerbet, Klaus Röbenack
Format:	Article
Language:	English
Published:	MDPI AG 2021-08-01
Series:	Algorithms
Subjects:	identification identifiability observability polynomial dynamical systems algebraic methods Lie derivative
Online Access:	https://www.mdpi.com/1999-4893/14/9/255

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spelling	doaj-5d13694e4db8428b942046250d8162252021-09-25T23:35:06ZengMDPI AGAlgorithms1999-48932021-08-011425525510.3390/a14090255An Algebraic Approach to IdentifiabilityDaniel Gerbet0Klaus Röbenack1Institute of Control Theory, Faculty of Electrical and Computer Engineering, Technische Universität Dresden, 01062 Dresden, GermanyInstitute of Control Theory, Faculty of Electrical and Computer Engineering, Technische Universität Dresden, 01062 Dresden, GermanyThis paper addresses the problem of identifiability of nonlinear polynomial state-space systems. Such systems have already been studied via the input-output equations, a description that, in general, requires differential algebra. The authors use a different algebraic approach, which is based on distinguishability and observability. Employing techniques from algebraic geometry such as polynomial ideals and Gröbner bases, local as well as global results are derived. The methods are illustrated on some example systems.https://www.mdpi.com/1999-4893/14/9/255identificationidentifiabilityobservabilitypolynomial dynamical systemsalgebraic methodsLie derivative
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Daniel Gerbet Klaus Röbenack
spellingShingle	Daniel Gerbet Klaus Röbenack An Algebraic Approach to Identifiability Algorithms identification identifiability observability polynomial dynamical systems algebraic methods Lie derivative
author_facet	Daniel Gerbet Klaus Röbenack
author_sort	Daniel Gerbet
title	An Algebraic Approach to Identifiability
title_short	An Algebraic Approach to Identifiability
title_full	An Algebraic Approach to Identifiability
title_fullStr	An Algebraic Approach to Identifiability
title_full_unstemmed	An Algebraic Approach to Identifiability
title_sort	algebraic approach to identifiability
publisher	MDPI AG
series	Algorithms
issn	1999-4893
publishDate	2021-08-01
description	This paper addresses the problem of identifiability of nonlinear polynomial state-space systems. Such systems have already been studied via the input-output equations, a description that, in general, requires differential algebra. The authors use a different algebraic approach, which is based on distinguishability and observability. Employing techniques from algebraic geometry such as polynomial ideals and Gröbner bases, local as well as global results are derived. The methods are illustrated on some example systems.
topic	identification identifiability observability polynomial dynamical systems algebraic methods Lie derivative
url	https://www.mdpi.com/1999-4893/14/9/255
work_keys_str_mv	AT danielgerbet analgebraicapproachtoidentifiability AT klausrobenack analgebraicapproachtoidentifiability AT danielgerbet algebraicapproachtoidentifiability AT klausrobenack algebraicapproachtoidentifiability
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An Algebraic Approach to Identifiability

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