Optimal Input Signals for Parameter Estimation - In Linear Systems with Spatio-Temporal Dynamics

by Ewaryst Rafajłowicz
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Ewaryst Rafajłowicz Optimal Input Signals for Parameter Estimation - In Linear Systems with Spatio-Temporal Dynamics
Ewaryst Rafajłowicz - Optimal Input Signals for Parameter Estimation - In Linear Systems with Spatio-Temporal Dynamics

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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.

Contributors

Author:
Ewaryst Rafajłowicz

Further information

Illustrations Note:
40 b/w ill., 10 b/w tbl.
Biography Artist:
Ewaryst Rafajlowicz, Wroclaw University of Science and Technology, Poland.
Language:
English
Edition:
1
Number of Pages:
202
Media Type:
Hardcover
Publisher:
De Gruyter

Master Data

Product Type:
Hardback book
Release date:
29 January 2022
Package Dimensions:
0.242 x 0.175 x 0.019 m; 0.47 kg
GTIN:
09783110350890
DUIN:
I0I1D55P4FQ
£82.05
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