Abstract: We study the problem of synthesis of lumped sources
control for the objects with distributed parameters on the basis of
continuous observation of phase state at given points of object. In the
proposed approach the phase state space (phase space) is beforehand
somehow partitioned at observable points into given subsets (zones).
The synthesizing control actions therewith are taken from the class of
piecewise constant functions. The current values of control actions
are determined by the subset of phase space that contains the
aggregate of current states of object at the observable points (in these
states control actions take constant values). In the paper such
synthesized control actions are called zone control actions. A
technique to obtain optimal values of zone control actions with the
use of smooth optimization methods is given. With this aim, the
formulas of objective functional gradient in the space of zone control
actions are obtained.