  The paper addresses the problem of optimization of a guaranteed (worst case)
result for a control system driven by a controlling side in presence of a
dynamical disturbance. The disturbances as functions of time are subject to
functional constraints belonging to a given family of constraints. The latter
family is known to the controlling side that does not observe the disturbance
and uses full-memory strategies to form the control actions. The study is
focused on the case where disturbance varies in open-loop disturbances chosen
in advance and the case where the disturbances are restricted to a
$L_2$--compact set fixed in advance but unknown to the controlling side. In
these cases it is shown that the optimal guaranteed result is non-improvable in
the sense that it coincides with that obtained in the class of quasi-strategies
-- nonantisipatory transformations of disturbances into controls. An
$\varepsilon$--optimal full-memory strategy is constructed. An illustrative
nonlinear example is given.
