EAN: 9783110350890

OPTIMAL INPUT SIGNALS FOR PARAMETER ESTIMATION ...

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.

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