This book provides, in a unified framework, an updated and

rather comprehensive treatment contered on the theory of ot-

pimal control with quadratic cost functional for abstract

linear systems with application to boundary/point control

problems for partial differential equations (distributed pa-

rameter systems).

The book culminates with the analysisof differential and

algebraic Riccati equations which arise in the pointwisefe-

edback synthesis of the optimal pair. It incorporates the

critical topics of optimal irregularity of solutions to mi-

xed problems for partial differential equations, exact con-

trollability, and uniform feedback stabilization. It covers

the main results of the theory - which has reached a consi-

derable degree of maturity over the last few years - as well

asthe authors' basic philosophy behind it.

Moreover, it provides numerous illustrative examples of

boundary/point control problems for partial differential

equations, where the abstract theory applies. However, in

line with the purpose of the manuscript, many technical pro-

ofs are referred to in the literature. Thus, the manuscript

should prove useful not only to mathematicians and theoreti-

cal scientists with expertise in partial differential equa-

tions, operator theory, numerical analysis, control theory,

etc., but also to those who simple wish to orient themselves

with the scope and status of the theory presently available.

Both continuous theory and numerical approximation theory

thereof are included.