This work is a revised and enlarged edition of a book with the same
title published in Romanian by the Publishing House of the Romanian
Academy in 1989. It grew out of lecture notes for a graduate course
given by the author at the University if Ia i and was initially intended
for students and readers primarily interested in applications of optimal
control of ordinary differential equations. In this vision the book had
to contain an elementary description of the Pontryagin maximum principle
and a large number of examples and applications from various fields of
science. The evolution of control science in the last decades has shown
that its meth- ods and tools are drawn from a large spectrum of
mathematical results which go beyond the classical theory of ordinary
differential equations and real analy- ses. Mathematical areas such as
functional analysis, topology, partial differential equations and
infinite dimensional dynamical systems, geometry, played and will
continue to play an increasing role in the development of the control
sciences. On the other hand, control problems is a rich source of deep
mathematical problems. Any presentation of control theory which for the
sake of accessibility ignores these facts is incomplete and unable to
attain its goals. This is the reason we considered necessary to widen
the initial perspective of the book and to include a rigorous
mathematical treatment of optimal control theory of processes governed
by ordi- nary differential equations and some typical problems from
theory of distributed parameter systems.
