Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a...

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Autor principal:	Simone Fiori
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	first-order and second-order abstract systems feedback control system smooth manifolds Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/69378a0b84d541b89fe55b643512259f
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id	oai:doaj.org-article:69378a0b84d541b89fe55b643512259f
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spelling	oai:doaj.org-article:69378a0b84d541b89fe55b643512259f2021-11-25T19:06:41ZManifold Calculus in System Theory and Control—Fundamentals and First-Order Systems10.3390/sym131120922073-8994https://doaj.org/article/69378a0b84d541b89fe55b643512259f2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2092https://doaj.org/toc/2073-8994The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.Simone FioriMDPI AGarticlefirst-order and second-order abstract systemsfeedback control systemsmooth manifoldsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2092, p 2092 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	first-order and second-order abstract systems feedback control system smooth manifolds Mathematics QA1-939
spellingShingle	first-order and second-order abstract systems feedback control system smooth manifolds Mathematics QA1-939 Simone Fiori Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems
description	The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.
format	article
author	Simone Fiori
author_facet	Simone Fiori
author_sort	Simone Fiori
title	Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems
title_short	Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems
title_full	Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems
title_fullStr	Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems
title_full_unstemmed	Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems
title_sort	manifold calculus in system theory and control—fundamentals and first-order systems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/69378a0b84d541b89fe55b643512259f
work_keys_str_mv	AT simonefiori manifoldcalculusinsystemtheoryandcontrolfundamentalsandfirstordersystems
_version_	1718410282731044864

Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

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