Topological Obstructions to Stability and Stabilization
This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topo...
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| Médium: | Online |
| Jazyk: | angličtina |
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Springer Nature
2023
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| On-line přístup: | ONIX_20230620_9783031301339_3 |
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| _version_ | 1869527585891811328 |
|---|---|
| author | Jongeneel, Wouter Moulay, Emmanuel |
| author_browse | Jongeneel, Wouter Moulay, Emmanuel |
| author_facet | Jongeneel, Wouter Moulay, Emmanuel |
| author_sort | Jongeneel, Wouter |
| collection | Directory of Open Access Books |
| description | This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk’s retraction theory and the index-theoretic methodology of Krasnosel’skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields. |
| format | Online |
| id | doab-20.500.12854ir-101656 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1016562025-07-17T10:01:14Z Topological Obstructions to Stability and Stabilization Jongeneel, Wouter Moulay, Emmanuel Control Systems Feedback Control Algebraic Topology Differential Topology Index Theory Retractive Theory Topological Obstruction thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TJ Electronics and communications engineering::TJF Electronics engineering::TJFM Automatic control engineering thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWR Nonlinear science thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TG Mechanical engineering and materials::TGM Materials science thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence thema EDItEUR::U Computing and Information Technology::UM Computer programming / software engineering::UMB Algorithms and data structures thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TJ Electronics and communications engineering::TJF Electronics engineering::TJFM Automatic control engineering thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWR Nonlinear science thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TG Mechanical engineering and materials::TGM Materials science thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence thema EDItEUR::U Computing and Information Technology::UM Computer programming / software engineering::UMB Algorithms and data structures This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk’s retraction theory and the index-theoretic methodology of Krasnosel’skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields. 2023-07-19T09:03:02Z 2023-07-19T09:03:02Z 2023-06-20T10:21:15Z 2023 book ONIX_20230620_9783031301339_3 https://library.oapen.org/handle/20.500.12657/63535 9783031301339 9783031301322 https://directory.doabooks.org/handle/20.500.12854/101656 eng SpringerBriefs in Electrical and Computer Engineering; SpringerBriefs in Control, Automation and Robotics open access image/jpeg image/jpeg n/a n/a https://library.oapen.org/bitstream/20.500.12657/63535/1/978-3-031-30133-9.pdf https://library.oapen.org/bitstream/20.500.12657/63535/1/978-3-031-30133-9.pdf Springer Nature Springer Nature Switzerland 10.1007/978-3-031-30133-9 10.1007/978-3-031-30133-9 9fa3421d-f917-4153-b9ab-fc337c396b5a Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung 07f61e34-5b96-49f0-9860-c87dd8228f26 9783031301339 9783031301322 Swiss National Science Foundation (SNF) Springer Nature Switzerland 132 Cham [...] open access |
| spellingShingle | Control Systems Feedback Control Algebraic Topology Differential Topology Index Theory Retractive Theory Topological Obstruction thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TJ Electronics and communications engineering::TJF Electronics engineering::TJFM Automatic control engineering thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWR Nonlinear science thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TG Mechanical engineering and materials::TGM Materials science thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence thema EDItEUR::U Computing and Information Technology::UM Computer programming / software engineering::UMB Algorithms and data structures thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TJ Electronics and communications engineering::TJF Electronics engineering::TJFM Automatic control engineering thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWR Nonlinear science thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TG Mechanical engineering and materials::TGM Materials science thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence thema EDItEUR::U Computing and Information Technology::UM Computer programming / software engineering::UMB Algorithms and data structures Jongeneel, Wouter Moulay, Emmanuel Topological Obstructions to Stability and Stabilization |
| title | Topological Obstructions to Stability and Stabilization |
| title_full | Topological Obstructions to Stability and Stabilization |
| title_fullStr | Topological Obstructions to Stability and Stabilization |
| title_full_unstemmed | Topological Obstructions to Stability and Stabilization |
| title_short | Topological Obstructions to Stability and Stabilization |
| title_sort | topological obstructions to stability and stabilization |
| topic | Control Systems Feedback Control Algebraic Topology Differential Topology Index Theory Retractive Theory Topological Obstruction thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TJ Electronics and communications engineering::TJF Electronics engineering::TJFM Automatic control engineering thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWR Nonlinear science thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TG Mechanical engineering and materials::TGM Materials science thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence thema EDItEUR::U Computing and Information Technology::UM Computer programming / software engineering::UMB Algorithms and data structures thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TJ Electronics and communications engineering::TJF Electronics engineering::TJFM Automatic control engineering thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWR Nonlinear science thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TG Mechanical engineering and materials::TGM Materials science thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence thema EDItEUR::U Computing and Information Technology::UM Computer programming / software engineering::UMB Algorithms and data structures |
| topic_facet | Control Systems Feedback Control Algebraic Topology Differential Topology Index Theory Retractive Theory Topological Obstruction thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TJ Electronics and communications engineering::TJF Electronics engineering::TJFM Automatic control engineering thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWR Nonlinear science thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TG Mechanical engineering and materials::TGM Materials science thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence thema EDItEUR::U Computing and Information Technology::UM Computer programming / software engineering::UMB Algorithms and data structures thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TJ Electronics and communications engineering::TJF Electronics engineering::TJFM Automatic control engineering thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWR Nonlinear science thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TG Mechanical engineering and materials::TGM Materials science thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence thema EDItEUR::U Computing and Information Technology::UM Computer programming / software engineering::UMB Algorithms and data structures |
| url | ONIX_20230620_9783031301339_3 |
| work_keys_str_mv | AT jongeneelwouter topologicalobstructionstostabilityandstabilization AT moulayemmanuel topologicalobstructionstostabilityandstabilization |