The idea of optimization runs through most parts of control theory.
The simplest optimal controls are preplanned (programmed) ones. The
problem of constructing optimal preplanned controls has been
extensively worked out in literature (see, e. g., the Pontrjagin
maximum principle giving necessary conditions of preplanned control
optimality). However, the concept of op timality itself has a
restrictive character: it is limited by what one means under
optimality in each separate case. The internal contradictoriness of
the preplanned control optimality ("the better is the enemy of the
good") yields that the practical significance of optimal preplanned
controls proves to be not great: such controls are usually
sensitive to unregistered disturbances (includ ing the round-off
errors which are inevitable when computer devices are used for
forming controls), as there is the effect of disturbance
accumulation in the control process which makes controls to be of
little use on large time inter vals. This gap is mainly provoked by
oversimplified settings of optimization problems. The outstanding
result of control theory established in the end of the first half
of our century is that controls in feedback form ensure the weak
sensitivity of closed loop systems with respect to "small"
unregistered internal and external disturbances acting in them
(here we do not need to discuss performance indexes, since the
considered phenomenon is of general nature). But by far not all
optimal preplanned controls can be represented in a feedback form."
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