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(t1, x))dx, (1) x0 with constraints zt = Д^xzyX (Xx) eD = t1] x ^xl], (2) x, y(t, x) = J g (t, x, s, z(t, s))ds, x e[ x0, xj, x0 x (3) z(t0, x) = J F (x, s, z(t0, s), v(s))ds. x0 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, t0, t1, x0, x1 (t0 ^ /-J; xQ ^ x1 ^ are given, ф(x, z) is a scalar function continuous with respect to all the variables together with the x, 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 Rr, x e [x0,x1]. Our goal is to derive a necessary optimality condition in the problem under consideration.