There is an ever-growing interest in control problems today, con- nected
with the urgent problems of the effective use of natural resources,
manpower, materials, and technology. When referring to the most
important achievements of science and technology in the 20th Century,
one usually mentions the splitting of the atom, the exploration of
space, and computer engineering. Achievements in control theory seem
less spectacular when viewed against this background, but the
applications of control theory are playing an important role in the
development of modern civilization, and there is every reason to believe
that this role will be even more signifi- cant in the future. Wherever
there is active human participation, the problem arises of finding the
best, or optimal, means of control. The demands of economics and
technology have given birth to optimization problems which, in turn,
have created new branches of mathematics. In the Forties, the
investigation of problems of economics gave rise to a new branch of
mathematical analysis called linear and convex program- ming. At that
time, problems of controlling flying vehicles and technolog- ical
processes of complex structures became important. A mathematical theory
was formulated in the mid-Fifties known as optimal control theory. Here
the maximum principle of L. S. Pontryagin played a pivotal role. Op-
timal control theory synthesized the concepts and methods of
investigation using the classical methods of the calculus of variations
and the methods of contemporary mathematics, for which Soviet
mathematicians made valuable contributions.
