Originally published in 2000, this is the first volume of a
comprehensive two-volume treatment of quadratic optimal control
theory for partial differential equations over a finite or infinite
time horizon, and related differential (integral) and algebraic
Riccati equations. Both continuous theory and numerical
approximation theory are included. The authors use an abstract
space, operator theoretic approach, which is based on semigroups
methods, and which is unifying across a few basic classes of
evolution. The various abstract frameworks are motivated by, and
ultimately directed to, partial differential equations with
boundary/point control. Volume 1 includes the abstract parabolic
theory for the finite and infinite cases and corresponding PDE
illustrations as well as various abstract hyperbolic settings in
the finite case. It presents numerous fascinating results. These
volumes will appeal to graduate students and researchers in pure
and applied mathematics and theoretical engineering with an
interest in optimal control problems.
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