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.
General
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