Optimal Input Signals for Parameter Estimation : : In Linear Systems with Spatio-Temporal Dynamics / / Ewaryst Rafajłowicz.
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 regr...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2022] ©2022 |
Year of Publication: | 2022 |
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Rafajłowicz, Ewaryst, author. aut http://id.loc.gov/vocabulary/relators/aut Optimal Input Signals for Parameter Estimation : In Linear Systems with Spatio-Temporal Dynamics / Ewaryst Rafajłowicz. Berlin ; Boston : De Gruyter, [2022] ©2022 1 online resource (XVIII, 184 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Preface -- Acknowledgements -- Contents -- List of Tables -- List of Figures -- Frequently used acronyms -- 1 Introduction -- 2 Optimal experiment design for linear regression models – a primer -- 3 Numerical search for D-optimal designs – basic methods for a linear regression -- 4 The product of experiment designs and its optimality -- 5 Optimal input signals for linear systems described by ODEs -- 6 Optimal excitations for systems described by elliptic equations -- 7 Optimal input signals for DPS – time domain synthesis -- 8 Input signal design for systems with spatio-temporal dynamics – frequency domain approach -- 9 Final comments -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 01. Dez 2022) Experimentendesign. Lineares System. Parameterabschätzung. Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1 9783110766820 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2022 English 9783110993899 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2022 9783110994810 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2022 English 9783110993868 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2022 9783110770445 ZDB-23-DMA EPUB 9783110383348 print 9783110350890 https://doi.org/10.1515/9783110351040 https://www.degruyter.com/isbn/9783110351040 Cover https://www.degruyter.com/document/cover/isbn/9783110351040/original |
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author |
Rafajłowicz, Ewaryst, Rafajłowicz, Ewaryst, |
spellingShingle |
Rafajłowicz, Ewaryst, Rafajłowicz, Ewaryst, Optimal Input Signals for Parameter Estimation : In Linear Systems with Spatio-Temporal Dynamics / Frontmatter -- Preface -- Acknowledgements -- Contents -- List of Tables -- List of Figures -- Frequently used acronyms -- 1 Introduction -- 2 Optimal experiment design for linear regression models – a primer -- 3 Numerical search for D-optimal designs – basic methods for a linear regression -- 4 The product of experiment designs and its optimality -- 5 Optimal input signals for linear systems described by ODEs -- 6 Optimal excitations for systems described by elliptic equations -- 7 Optimal input signals for DPS – time domain synthesis -- 8 Input signal design for systems with spatio-temporal dynamics – frequency domain approach -- 9 Final comments -- Bibliography -- Index |
author_facet |
Rafajłowicz, Ewaryst, Rafajłowicz, Ewaryst, |
author_variant |
e r er e r er |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Rafajłowicz, Ewaryst, |
title |
Optimal Input Signals for Parameter Estimation : In Linear Systems with Spatio-Temporal Dynamics / |
title_sub |
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_auth |
Optimal Input Signals for Parameter Estimation : In Linear Systems with Spatio-Temporal Dynamics / |
title_alt |
Frontmatter -- Preface -- Acknowledgements -- Contents -- List of Tables -- List of Figures -- Frequently used acronyms -- 1 Introduction -- 2 Optimal experiment design for linear regression models – a primer -- 3 Numerical search for D-optimal designs – basic methods for a linear regression -- 4 The product of experiment designs and its optimality -- 5 Optimal input signals for linear systems described by ODEs -- 6 Optimal excitations for systems described by elliptic equations -- 7 Optimal input signals for DPS – time domain synthesis -- 8 Input signal design for systems with spatio-temporal dynamics – frequency domain approach -- 9 Final comments -- Bibliography -- Index |
title_new |
Optimal Input Signals for Parameter Estimation : |
title_sort |
optimal input signals for parameter estimation : in linear systems with spatio-temporal dynamics / |
publisher |
De Gruyter, |
publishDate |
2022 |
physical |
1 online resource (XVIII, 184 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- Acknowledgements -- Contents -- List of Tables -- List of Figures -- Frequently used acronyms -- 1 Introduction -- 2 Optimal experiment design for linear regression models – a primer -- 3 Numerical search for D-optimal designs – basic methods for a linear regression -- 4 The product of experiment designs and its optimality -- 5 Optimal input signals for linear systems described by ODEs -- 6 Optimal excitations for systems described by elliptic equations -- 7 Optimal input signals for DPS – time domain synthesis -- 8 Input signal design for systems with spatio-temporal dynamics – frequency domain approach -- 9 Final comments -- Bibliography -- Index |
isbn |
9783110351040 9783110766820 9783110993899 9783110994810 9783110993868 9783110770445 9783110383348 9783110350890 |
url |
https://doi.org/10.1515/9783110351040 https://www.degruyter.com/isbn/9783110351040 https://www.degruyter.com/document/cover/isbn/9783110351040/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
519 - Probabilities & applied mathematics |
dewey-full |
519.544 |
dewey-sort |
3519.544 |
dewey-raw |
519.544 |
dewey-search |
519.544 |
doi_str_mv |
10.1515/9783110351040 |
oclc_num |
1306057676 |
work_keys_str_mv |
AT rafajłowiczewaryst optimalinputsignalsforparameterestimationinlinearsystemswithspatiotemporaldynamics |
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n |
ids_txt_mv |
(DE-B1597)253107 (OCoLC)1306057676 |
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cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2022 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2022 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2022 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2022 |
is_hierarchy_title |
Optimal Input Signals for Parameter Estimation : In Linear Systems with Spatio-Temporal Dynamics / |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1 |
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1806144364318031872 |
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