About one control problem described by system of inteqro-diferential equations
Consider the problem of minimizing the functional of terminal type S (v) = J ф(х, z(t<sub>1</sub>, x))dx, (1) <sup>x</sup>0 with constraints <sup>z</sup>t = Д^xzyX (X<sup>x) e</sup>D = <sup>t</sup>1<sup>] x</sup> ^<sup>x</sup>l<sup>],</sup> (2) x, y(t, x) = J g (t, x, s, z(t, s))ds, x e[ x<sub>0</sub>, xj, <sup>x</sup>0 <sub>x</sub> (3) z(t<sub>0</sub>, x) = J F (x, s, z(t<sub>0</sub>, s), v(s))ds. <sup>x</sup>0 Here f (t, x, z, y), g(t, x, s, z) is the given n- and m-dimensional vector functions respectively, continuous with respect to all the variables together with partial derivatives of the vectors of state, F (x, z, v) is the given n-dimensional vector-function continuous with respect to all the variables together with partial derivatives z, t<sub>0</sub>, t<sub>1</sub>, x<sub>0</sub>, x<sub>1</sub> (t<sub>0</sub> ^ /-J; xQ ^ x1 ^ are given, ф(x, z) is a scalar function continuous with respect to all the variables together with the <sup>x,</sup> z), v = v (x) is piecewise continuous (with a finite number of points dz of discontinuity of the first kind) vector control actions with values from a specified non-empty and bounded set that is, v(x) eV с R<sup>r</sup>, x e [x<sub>0</sub>,x<sub>1</sub>]. Our goal is to derive a necessary optimality condition in the problem under consideration.