Optimal Input Signals for Parameter Estimation: In Linear Systems with Spatio-Te

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Optimal Input Signals for Parameter Estimation by Ewaryst Rafajłowicz

The aim of this book is to prove an overview of classic results on optimal experiment design for estimating parameters of a regression function, and to indicate how to use them for sensors' allocation problems for estimating parameters in systems

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

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.
  

Details ISBN3110350890 Short Title Optimal Input Signals for Parameter Estimation Publisher De Gruyter Language English ISBN-10 3110350890 ISBN-13 9783110350890 Format Hardcover Subtitle In Linear Systems with Spatio-Temporal Dynamics Year 2022 Imprint De Gruyter Place of Publication Berlin Country of Publication Germany Publication Date 2022-03-21 Pages 202 UK Release Date 2022-03-21 Author Ewaryst Rafajowicz Alternative 9783110351040 DEWEY 519.544 Audience Professional & Vocational Country of Origin DE Product Class Description Mathematics Illustrations 40 Illustrations; 10 Tables, black and white
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