Conic Nonholonomic Constraints on Surfaces and Control Systems
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| Titel: | Conic Nonholonomic Constraints on Surfaces and Control Systems |
|---|---|
| Autoren: | Schmoderer, Timothée, Respondek, Witold |
| Weitere Verfasser: | SCHMODERER, Timothée, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire pluridisciplinaire de recherche en ingénierie des systèmes, mécanique et énergétique (PRISME), Université d'Orléans (UO)-Institut National des Sciences Appliquées - Centre Val de Loire (INSA CVL), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Institute of Automatic Control |
| Quelle: | Journal of Dynamical and Control Systems. 29:1981-2022 |
| Publication Status: | Preprint |
| Verlagsinformationen: | Springer Science and Business Media LLC, 2023. |
| Publikationsjahr: | 2023 |
| Schlagwörter: | Mathematics - Differential Geometry, feedback equivalence, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], nonlinear control system, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Dynamical Systems (math.DS), nonholonomic constraint, 01 natural sciences, 93B52, 37N35, 93A10, 93B27, 53B20, 53B30, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Optimization and Control (math.OC), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, normal forms, FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], pseudo-Riemannian geometry, Mathematics - Dynamical Systems, 0101 mathematics, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG], [INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering, Mathematics - Optimization and Control, conic submanifolds |
| Beschreibung: | This paper addresses the equivalence problem of conic submanifolds in the tangent bundle of a smooth 2-dimensional manifold. Those are given by a quadratic relation between the velocities and are treated as nonholonomic constraints whose admissible curves are trajectories of the corresponding control systems, called quadratic systems. We deal with the problem of characterising and classifying conic submanifolds under the prism of feedback equivalence of control systems, both control-affine and fully nonlinear. The first main result of this work is a complete description of non-degenerate conic submanifolds via a characterisation under feedback transformations of the novel class of quadratic control-affine systems. This characterisation can explicitly be tested on structure functions defined for any control-affine system and gives a normal form of quadratizable systems and of conic submanifolds. Then, we consider the classification problem of regular conic submanifolds (ellipses, hyperbolas, and parabolas), which is treated via feedback classification of quadratic control-nonlinear systems. Our classification includes several normal forms of quadratic systems (in particular, normal forms not containing functional parameters as well as those containing neither functional nor real parameters), and, as a consequence, gives a classification of regular conic submanifolds. 30 pages, 5 appendices, preprint |
| Publikationsart: | Article Conference object |
| Dateibeschreibung: | application/pdf |
| Sprache: | English |
| ISSN: | 1573-8698 1079-2724 |
| DOI: | 10.1007/s10883-023-09659-9 |
| DOI: | 10.48550/arxiv.2106.08635 |
| Zugangs-URL: | http://arxiv.org/abs/2106.08635 https://normandie-univ.hal.science/hal-04032788v1 https://normandie-univ.hal.science/hal-03634034v3/document https://normandie-univ.hal.science/hal-03634034v3 https://doi.org/10.1007/s10883-023-09659-9 |
| Rights: | Springer Nature TDM CC BY NC SA |
| Dokumentencode: | edsair.doi.dedup.....7a9cbed7e0a63894ca6f317661e7e16b |
| Datenbank: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | This paper addresses the equivalence problem of conic submanifolds in the tangent bundle of a smooth 2-dimensional manifold. Those are given by a quadratic relation between the velocities and are treated as nonholonomic constraints whose admissible curves are trajectories of the corresponding control systems, called quadratic systems. We deal with the problem of characterising and classifying conic submanifolds under the prism of feedback equivalence of control systems, both control-affine and fully nonlinear. The first main result of this work is a complete description of non-degenerate conic submanifolds via a characterisation under feedback transformations of the novel class of quadratic control-affine systems. This characterisation can explicitly be tested on structure functions defined for any control-affine system and gives a normal form of quadratizable systems and of conic submanifolds. Then, we consider the classification problem of regular conic submanifolds (ellipses, hyperbolas, and parabolas), which is treated via feedback classification of quadratic control-nonlinear systems. Our classification includes several normal forms of quadratic systems (in particular, normal forms not containing functional parameters as well as those containing neither functional nor real parameters), and, as a consequence, gives a classification of regular conic submanifolds.<br />30 pages, 5 appendices, preprint |
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| ISSN: | 15738698 10792724 |
| DOI: | 10.1007/s10883-023-09659-9 |