Flatness-based control revisited: The HEOL setting
We present the algebraic foundations of the HEOL setting, which combines flatness-based control and intelligent controllers, two advances in automatic control that have been proven in practice, including in industry. The result provides a solution to many pending questions on feedback loops concerni...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.674/ |
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| author | Join, Cédric Delaleau, Emmanuel Fliess, Michel |
| author_facet | Join, Cédric Delaleau, Emmanuel Fliess, Michel |
| author_sort | Join, Cédric |
| collection | DOAJ |
| description | We present the algebraic foundations of the HEOL setting, which combines flatness-based control and intelligent controllers, two advances in automatic control that have been proven in practice, including in industry. The result provides a solution to many pending questions on feedback loops concerning flatness-based control and model-free control (MFC). Elementary module theory, ordinary differential fields and the generalization of Kähler differentials to differential fields provide an intrinsic definition of the tangent linear system. The algebraic manipulations associated with the operational calculus lead to homeostat and intelligent controllers. They are illustrated via some computer simulations. |
| format | Article |
| id | doaj-art-57a9ee0373c64c838e2aedcbc20292f0 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-57a9ee0373c64c838e2aedcbc20292f02025-02-07T11:26:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G121693170610.5802/crmath.67410.5802/crmath.674Flatness-based control revisited: The HEOL settingJoin, Cédric0https://orcid.org/0000-0001-6304-1262Delaleau, Emmanuel1https://orcid.org/0000-0002-0257-568XFliess, Michel2https://orcid.org/0000-0003-3426-3637AL.I.E.N., 7 rue Maurice Barrès, 54330 Vézelise, France; CRAN (CNRS, UMR 7039), Université de Lorraine, Campus Aiguillettes, BP 70239, 54506 Vandœuvre-lès-Nancy, FranceENI Brest, UMR CNRS 6027, IRDL, 29200 Brest, FranceAL.I.E.N., 7 rue Maurice Barrès, 54330 Vézelise, France; LIX (CNRS, UMR 7161), École polytechnique, 91128 Palaiseau, FranceWe present the algebraic foundations of the HEOL setting, which combines flatness-based control and intelligent controllers, two advances in automatic control that have been proven in practice, including in industry. The result provides a solution to many pending questions on feedback loops concerning flatness-based control and model-free control (MFC). Elementary module theory, ordinary differential fields and the generalization of Kähler differentials to differential fields provide an intrinsic definition of the tangent linear system. The algebraic manipulations associated with the operational calculus lead to homeostat and intelligent controllers. They are illustrated via some computer simulations.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.674/Flatness-based controlmodel-free controlintelligent controllersdifferential algebramodule theory |
| spellingShingle | Join, Cédric Delaleau, Emmanuel Fliess, Michel Flatness-based control revisited: The HEOL setting Comptes Rendus. Mathématique Flatness-based control model-free control intelligent controllers differential algebra module theory |
| title | Flatness-based control revisited: The HEOL setting |
| title_full | Flatness-based control revisited: The HEOL setting |
| title_fullStr | Flatness-based control revisited: The HEOL setting |
| title_full_unstemmed | Flatness-based control revisited: The HEOL setting |
| title_short | Flatness-based control revisited: The HEOL setting |
| title_sort | flatness based control revisited the heol setting |
| topic | Flatness-based control model-free control intelligent controllers differential algebra module theory |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.674/ |
| work_keys_str_mv | AT joincedric flatnessbasedcontrolrevisitedtheheolsetting AT delaleauemmanuel flatnessbasedcontrolrevisitedtheheolsetting AT fliessmichel flatnessbasedcontrolrevisitedtheheolsetting |