Control Theory from the Geometric Viewpoint:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Schriftenreihe: | Encyclopaedia of Mathematical Sciences, Control Theory and Optimization II
87 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com pletely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for "free will" in this fatalistic world, then we come to control systems. We do so by allowing certain param eters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological processes etc. We try to control all these dynamical systems! Smooth dynamical systems are governed by differential equations. In this book we deal only with finite dimensional systems: they are governed by ordi nary differential equations on finite dimensional smooth manifolds. A control system for us is thus a family of ordinary differential equations. The family is parametrized by control parameters |
| Beschreibung: | 1 Online-Ressource (XIV, 412 p) |
| ISBN: | 9783662064047 9783642059070 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-662-06404-7 |
Internformat
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Agrachev, Andrei A. |
| author_facet | Agrachev, Andrei A. |
| author_role | aut |
| author_sort | Agrachev, Andrei A. |
| author_variant | a a a aa aaa |
| building | Verbundindex |
| bvnumber | BV042423374 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863898833 (DE-599)BVBBV042423374 |
| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-06404-7 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662064047 9783642059070 |
| issn | 0938-0396 |
| language | English |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Encyclopaedia of Mathematical Sciences, Control Theory and Optimization II |
| spelling | Agrachev, Andrei A. Verfasser aut Control Theory from the Geometric Viewpoint by Andrei A. Agrachev, Yuri L. Sachkov Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XIV, 412 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences, Control Theory and Optimization II 87 0938-0396 This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com pletely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for "free will" in this fatalistic world, then we come to control systems. We do so by allowing certain param eters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological processes etc. We try to control all these dynamical systems! Smooth dynamical systems are governed by differential equations. In this book we deal only with finite dimensional systems: they are governed by ordi nary differential equations on finite dimensional smooth manifolds. A control system for us is thus a family of ordinary differential equations. The family is parametrized by control parameters Mathematics Systems theory Systems Theory, Control Mathematik Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 s Differentialgeometrie (DE-588)4012248-7 s 1\p DE-604 Gewöhnliche Differentialgleichung (DE-588)4020929-5 s 2\p DE-604 Sachkov, Yuri L. Sonstige oth https://doi.org/10.1007/978-3-662-06404-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Agrachev, Andrei A. Control Theory from the Geometric Viewpoint Mathematics Systems theory Systems Theory, Control Mathematik Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4116671-1 (DE-588)4012248-7 (DE-588)4032317-1 |
| title | Control Theory from the Geometric Viewpoint |
| title_auth | Control Theory from the Geometric Viewpoint |
| title_exact_search | Control Theory from the Geometric Viewpoint |
| title_full | Control Theory from the Geometric Viewpoint by Andrei A. Agrachev, Yuri L. Sachkov |
| title_fullStr | Control Theory from the Geometric Viewpoint by Andrei A. Agrachev, Yuri L. Sachkov |
| title_full_unstemmed | Control Theory from the Geometric Viewpoint by Andrei A. Agrachev, Yuri L. Sachkov |
| title_short | Control Theory from the Geometric Viewpoint |
| title_sort | control theory from the geometric viewpoint |
| topic | Mathematics Systems theory Systems Theory, Control Mathematik Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Mathematics Systems theory Systems Theory, Control Mathematik Gewöhnliche Differentialgleichung System von gewöhnlichen Differentialgleichungen Differentialgeometrie Kontrolltheorie |
| url | https://doi.org/10.1007/978-3-662-06404-7 |
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