Hankel Norm Approximation for Infinite-Dimensional Systems:
Model reduction is an important engineering problem in which one aims to replace an elaborate model by a simpler model without undue loss of accuracy. The accuracy can be mathematically measured in several possible norms and the Hankel norm is one such. The Hankel norm gives a meaningful notion of d...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2002
|
| Schriftenreihe: | Lecture Notes in Control and Information Sciences
277 |
| Schlagworte: | |
| Online-Zugang: | FHI01 BTU01 URL des Erstveröffentlichers |
| Zusammenfassung: | Model reduction is an important engineering problem in which one aims to replace an elaborate model by a simpler model without undue loss of accuracy. The accuracy can be mathematically measured in several possible norms and the Hankel norm is one such. The Hankel norm gives a meaningful notion of distance between two linear systems: roughly speaking, it is the induced norm of the operator that maps past inputs to future outputs. It turns out that the engineering problem of model reduction in the Hankel norm is closely related to the mathematical problem of finding solutions to the sub-optimal Nehari-Takagi problem, which is called "the sub-optimal Hankel norm approximation problem" in this book. Although the existence of a solution to the sub-optimal Hankel norm approximation problem has been known since the 1970s, this book presents explicit solutions and, in particular, new formulae for several large classes of infinite-dimensional systems for the first time |
| Beschreibung: | 1 Online-Ressource (VIII, 148 p) |
| ISBN: | 9783540458777 |
| DOI: | 10.1007/3-540-45877-8 |
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| 520 | |a Model reduction is an important engineering problem in which one aims to replace an elaborate model by a simpler model without undue loss of accuracy. The accuracy can be mathematically measured in several possible norms and the Hankel norm is one such. The Hankel norm gives a meaningful notion of distance between two linear systems: roughly speaking, it is the induced norm of the operator that maps past inputs to future outputs. It turns out that the engineering problem of model reduction in the Hankel norm is closely related to the mathematical problem of finding solutions to the sub-optimal Nehari-Takagi problem, which is called "the sub-optimal Hankel norm approximation problem" in this book. Although the existence of a solution to the sub-optimal Hankel norm approximation problem has been known since the 1970s, this book presents explicit solutions and, in particular, new formulae for several large classes of infinite-dimensional systems for the first time | ||
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| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| doi_str_mv | 10.1007/3-540-45877-8 |
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| id | DE-604.BV045149261 |
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| indexdate | 2024-07-10T08:10:03Z |
| institution | BVB |
| isbn | 9783540458777 |
| language | English |
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| spelling | Sasane, Amol Verfasser aut Hankel Norm Approximation for Infinite-Dimensional Systems by Amol Sasane Berlin, Heidelberg Springer Berlin Heidelberg 2002 1 Online-Ressource (VIII, 148 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Control and Information Sciences 277 Model reduction is an important engineering problem in which one aims to replace an elaborate model by a simpler model without undue loss of accuracy. The accuracy can be mathematically measured in several possible norms and the Hankel norm is one such. The Hankel norm gives a meaningful notion of distance between two linear systems: roughly speaking, it is the induced norm of the operator that maps past inputs to future outputs. It turns out that the engineering problem of model reduction in the Hankel norm is closely related to the mathematical problem of finding solutions to the sub-optimal Nehari-Takagi problem, which is called "the sub-optimal Hankel norm approximation problem" in this book. Although the existence of a solution to the sub-optimal Hankel norm approximation problem has been known since the 1970s, this book presents explicit solutions and, in particular, new formulae for several large classes of infinite-dimensional systems for the first time Engineering Control, Robotics, Mechatronics Complexity Systems Theory, Control Mathematical Methods in Physics Vibration, Dynamical Systems, Control System theory Physics Complexity, Computational Vibration Dynamical systems Dynamics Control engineering Robotics Mechatronics Approximation (DE-588)4002498-2 gnd rswk-swf Unendlichdimensionales System (DE-588)4207956-1 gnd rswk-swf Hankel-Operator (DE-588)4314042-7 gnd rswk-swf Lineares Differentialgleichungssystem (DE-588)4452554-0 gnd rswk-swf Ordnungsreduktion (DE-588)4136085-0 gnd rswk-swf Unendlichdimensionales System (DE-588)4207956-1 s Approximation (DE-588)4002498-2 s Hankel-Operator (DE-588)4314042-7 s 1\p DE-604 Lineares Differentialgleichungssystem (DE-588)4452554-0 s 2\p DE-604 Ordnungsreduktion (DE-588)4136085-0 s 3\p DE-604 Erscheint auch als Druck-Ausgabe 9783540433279 https://doi.org/10.1007/3-540-45877-8 Verlag URL des Erstveröffentlichers 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sasane, Amol Hankel Norm Approximation for Infinite-Dimensional Systems Engineering Control, Robotics, Mechatronics Complexity Systems Theory, Control Mathematical Methods in Physics Vibration, Dynamical Systems, Control System theory Physics Complexity, Computational Vibration Dynamical systems Dynamics Control engineering Robotics Mechatronics Approximation (DE-588)4002498-2 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd Hankel-Operator (DE-588)4314042-7 gnd Lineares Differentialgleichungssystem (DE-588)4452554-0 gnd Ordnungsreduktion (DE-588)4136085-0 gnd |
| subject_GND | (DE-588)4002498-2 (DE-588)4207956-1 (DE-588)4314042-7 (DE-588)4452554-0 (DE-588)4136085-0 |
| title | Hankel Norm Approximation for Infinite-Dimensional Systems |
| title_auth | Hankel Norm Approximation for Infinite-Dimensional Systems |
| title_exact_search | Hankel Norm Approximation for Infinite-Dimensional Systems |
| title_full | Hankel Norm Approximation for Infinite-Dimensional Systems by Amol Sasane |
| title_fullStr | Hankel Norm Approximation for Infinite-Dimensional Systems by Amol Sasane |
| title_full_unstemmed | Hankel Norm Approximation for Infinite-Dimensional Systems by Amol Sasane |
| title_short | Hankel Norm Approximation for Infinite-Dimensional Systems |
| title_sort | hankel norm approximation for infinite dimensional systems |
| topic | Engineering Control, Robotics, Mechatronics Complexity Systems Theory, Control Mathematical Methods in Physics Vibration, Dynamical Systems, Control System theory Physics Complexity, Computational Vibration Dynamical systems Dynamics Control engineering Robotics Mechatronics Approximation (DE-588)4002498-2 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd Hankel-Operator (DE-588)4314042-7 gnd Lineares Differentialgleichungssystem (DE-588)4452554-0 gnd Ordnungsreduktion (DE-588)4136085-0 gnd |
| topic_facet | Engineering Control, Robotics, Mechatronics Complexity Systems Theory, Control Mathematical Methods in Physics Vibration, Dynamical Systems, Control System theory Physics Complexity, Computational Vibration Dynamical systems Dynamics Control engineering Robotics Mechatronics Approximation Unendlichdimensionales System Hankel-Operator Lineares Differentialgleichungssystem Ordnungsreduktion |
| url | https://doi.org/10.1007/3-540-45877-8 |
| work_keys_str_mv | AT sasaneamol hankelnormapproximationforinfinitedimensionalsystems |