Theory of Chattering Control: with applications to Astronautics, Robotics, Economics, and Engineering
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1994
|
| Schriftenreihe: | Systems & Control: Foundations & Applications
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The common experience in solving control problems shows that optimal control as a function of time proves to be piecewise analytic, having a finite number of jumps (called switches) on any finite-time interval. Meanwhile there exists an old example proposed by A.T. Fuller [1961) in which optimal control has an infinite number of switches on a finite-time interval. This phenomenon is called chattering. It has become increasingly clear that chattering is widespread. This book is devoted to its exploration. Chattering obstructs the direct use of Pontryagin's maximum principle because of the lack of a nonzero-length interval with a continuous control function. That is why the common experience appears misleading. It is the hidden symmetry of Fuller's problem that allows the explicit solution. Namely, there exists a one-parameter group which respects the optimal trajectories of the problem. When published in 1961, Fuller's example incited curiosity, but it was considered only "interesting" and soon was forgotten. The second wave of attention to chattering was raised about 12 years later when several other examples with optimal chattering trajectories were 1 found. All these examples were two-dimensional with the one-parameter group of symmetries |
| Beschreibung: | 1 Online-Ressource (XVI, 244 p) |
| ISBN: | 9781461227021 9781461276340 |
| DOI: | 10.1007/978-1-4612-2702-1 |
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| 245 | 1 | 0 | |a Theory of Chattering Control |b with applications to Astronautics, Robotics, Economics, and Engineering |c by Michail I. Zelikin, Vladimir Borisov |
| 264 | 1 | |a Boston, MA |b Birkhäuser Boston |c 1994 | |
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| 500 | |a The common experience in solving control problems shows that optimal control as a function of time proves to be piecewise analytic, having a finite number of jumps (called switches) on any finite-time interval. Meanwhile there exists an old example proposed by A.T. Fuller [1961) in which optimal control has an infinite number of switches on a finite-time interval. This phenomenon is called chattering. It has become increasingly clear that chattering is widespread. This book is devoted to its exploration. Chattering obstructs the direct use of Pontryagin's maximum principle because of the lack of a nonzero-length interval with a continuous control function. That is why the common experience appears misleading. It is the hidden symmetry of Fuller's problem that allows the explicit solution. Namely, there exists a one-parameter group which respects the optimal trajectories of the problem. When published in 1961, Fuller's example incited curiosity, but it was considered only "interesting" and soon was forgotten. The second wave of attention to chattering was raised about 12 years later when several other examples with optimal chattering trajectories were 1 found. All these examples were two-dimensional with the one-parameter group of symmetries | ||
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-2702-1 |
| format | Electronic eBook |
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| id | DE-604.BV042420069 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461227021 9781461276340 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855486 |
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| physical | 1 Online-Ressource (XVI, 244 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1994 |
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| publisher | Birkhäuser Boston |
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| series2 | Systems & Control: Foundations & Applications |
| spelling | Zelikin, Michail I. Verfasser aut Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering by Michail I. Zelikin, Vladimir Borisov Boston, MA Birkhäuser Boston 1994 1 Online-Ressource (XVI, 244 p) txt rdacontent c rdamedia cr rdacarrier Systems & Control: Foundations & Applications The common experience in solving control problems shows that optimal control as a function of time proves to be piecewise analytic, having a finite number of jumps (called switches) on any finite-time interval. Meanwhile there exists an old example proposed by A.T. Fuller [1961) in which optimal control has an infinite number of switches on a finite-time interval. This phenomenon is called chattering. It has become increasingly clear that chattering is widespread. This book is devoted to its exploration. Chattering obstructs the direct use of Pontryagin's maximum principle because of the lack of a nonzero-length interval with a continuous control function. That is why the common experience appears misleading. It is the hidden symmetry of Fuller's problem that allows the explicit solution. Namely, there exists a one-parameter group which respects the optimal trajectories of the problem. When published in 1961, Fuller's example incited curiosity, but it was considered only "interesting" and soon was forgotten. The second wave of attention to chattering was raised about 12 years later when several other examples with optimal chattering trajectories were 1 found. All these examples were two-dimensional with the one-parameter group of symmetries Mathematics Mathematics, general Mathematik Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Optimale Kontrolle (DE-588)4121428-6 s 1\p DE-604 Borisov, Vladimir Sonstige oth https://doi.org/10.1007/978-1-4612-2702-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zelikin, Michail I. Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering Mathematics Mathematics, general Mathematik Optimale Kontrolle (DE-588)4121428-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4121428-6 (DE-588)4139943-2 |
| title | Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering |
| title_auth | Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering |
| title_exact_search | Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering |
| title_full | Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering by Michail I. Zelikin, Vladimir Borisov |
| title_fullStr | Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering by Michail I. Zelikin, Vladimir Borisov |
| title_full_unstemmed | Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering by Michail I. Zelikin, Vladimir Borisov |
| title_short | Theory of Chattering Control |
| title_sort | theory of chattering control with applications to astronautics robotics economics and engineering |
| title_sub | with applications to Astronautics, Robotics, Economics, and Engineering |
| topic | Mathematics Mathematics, general Mathematik Optimale Kontrolle (DE-588)4121428-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Optimale Kontrolle Hamiltonsches System |
| url | https://doi.org/10.1007/978-1-4612-2702-1 |
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