Optimal input signals for parameter estimation: in linear systems with spatio-temporal dynamics
The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE's as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Berlin ; Boston
De Gruyter
[2022]
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| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FHR01 FKE01 FLA01 TUM01 UBY01 UPA01 Volltext |
| Zusammenfassung: | The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE's as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for regression functions and in simple but useful results on the dependence of eigenvalues of partial differential operators on their parameters. Examples are provided that reveal sometimes intriguing geometry of spatiotemporal input signals and responses to them. An introduction to optimal experimental design for parameter estimation of regression functions is provided. The emphasis is on functions having a tensor product (Kronecker) structure that is compatible with eigenfunctions of many partial differential operators. New optimality conditions in the time domain and computational algorithms are derived for D-optimal input signals when parameters of ordinary differential equations are estimated. They are used as building blocks for constructing D-optimal spatio-temporal inputs for systems described by linear partial differential equations of the parabolic and hyperbolic types with constant parameters. Optimality conditions for spatially distributed signals are also obtained for equations of elliptic type in those cases where their eigenfunctions do not depend on unknown constant parameters. These conditions and the resulting algorithms are interesting in their own right and, moreover, they are second building blocks for optimality of spatio-temporal signals. A discussion of the generalizability and possible applications of the results obtained is presented |
| Beschreibung: | 1 Online-Ressource (XI, 184 Seiten) |
| ISBN: | 9783110351040 |
| DOI: | 10.1515/9783110351040 |
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| isbn | 9783110351040 |
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| spelling | Rafajłowicz, Ewaryst 1953- (DE-588)1262331668 aut Optimal input signals for parameter estimation in linear systems with spatio-temporal dynamics Ewaryst Rafajłowicz Berlin ; Boston De Gruyter [2022] © 2022 1 Online-Ressource (XI, 184 Seiten) txt rdacontent c rdamedia cr rdacarrier The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE's as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for regression functions and in simple but useful results on the dependence of eigenvalues of partial differential operators on their parameters. Examples are provided that reveal sometimes intriguing geometry of spatiotemporal input signals and responses to them. An introduction to optimal experimental design for parameter estimation of regression functions is provided. The emphasis is on functions having a tensor product (Kronecker) structure that is compatible with eigenfunctions of many partial differential operators. New optimality conditions in the time domain and computational algorithms are derived for D-optimal input signals when parameters of ordinary differential equations are estimated. They are used as building blocks for constructing D-optimal spatio-temporal inputs for systems described by linear partial differential equations of the parabolic and hyperbolic types with constant parameters. Optimality conditions for spatially distributed signals are also obtained for equations of elliptic type in those cases where their eigenfunctions do not depend on unknown constant parameters. These conditions and the resulting algorithms are interesting in their own right and, moreover, they are second building blocks for optimality of spatio-temporal signals. A discussion of the generalizability and possible applications of the results obtained is presented Experimentendesign Lineares System Parameterabschätzung Optimierung (DE-588)4043664-0 gnd rswk-swf Green-Funktion (DE-588)4158123-4 gnd rswk-swf Eingangssignal (DE-588)1079295801 gnd rswk-swf Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Eingangssignal (DE-588)1079295801 s Optimierung (DE-588)4043664-0 s Lineare partielle Differentialgleichung (DE-588)4167708-0 s Green-Funktion (DE-588)4158123-4 s DE-604 Erscheint auch als Druck-Ausgabe 9783110350890 https://doi.org/10.1515/9783110351040 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Rafajłowicz, Ewaryst 1953- Optimal input signals for parameter estimation in linear systems with spatio-temporal dynamics Experimentendesign Lineares System Parameterabschätzung Optimierung (DE-588)4043664-0 gnd Green-Funktion (DE-588)4158123-4 gnd Eingangssignal (DE-588)1079295801 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4158123-4 (DE-588)1079295801 (DE-588)4167708-0 |
| title | Optimal input signals for parameter estimation in linear systems with spatio-temporal dynamics |
| title_auth | Optimal input signals for parameter estimation in linear systems with spatio-temporal dynamics |
| title_exact_search | Optimal input signals for parameter estimation in linear systems with spatio-temporal dynamics |
| title_exact_search_txtP | Optimal input signals for parameter estimation in linear systems with spatio-temporal dynamics |
| title_full | Optimal input signals for parameter estimation in linear systems with spatio-temporal dynamics Ewaryst Rafajłowicz |
| title_fullStr | Optimal input signals for parameter estimation in linear systems with spatio-temporal dynamics Ewaryst Rafajłowicz |
| title_full_unstemmed | Optimal input signals for parameter estimation in linear systems with spatio-temporal dynamics Ewaryst Rafajłowicz |
| title_short | Optimal input signals for parameter estimation |
| title_sort | optimal input signals for parameter estimation in linear systems with spatio temporal dynamics |
| title_sub | in linear systems with spatio-temporal dynamics |
| topic | Experimentendesign Lineares System Parameterabschätzung Optimierung (DE-588)4043664-0 gnd Green-Funktion (DE-588)4158123-4 gnd Eingangssignal (DE-588)1079295801 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd |
| topic_facet | Experimentendesign Lineares System Parameterabschätzung Optimierung Green-Funktion Eingangssignal Lineare partielle Differentialgleichung |
| url | https://doi.org/10.1515/9783110351040 |
| work_keys_str_mv | AT rafajłowiczewaryst optimalinputsignalsforparameterestimationinlinearsystemswithspatiotemporaldynamics |