The paper studies control problems for the symmetrical system of two first-order differential equations in partial derivatives which are Friedrichs positive. One of the components on a sector of the boundary is taken as control. Functional to be minimized is the squared norm of the deviation from the solution of a given function on the other sector of the boundary. It is proposed to solve this problem by iterative gradient method. Functional gradient is found by solving a conjugative problem.

Key words: symmetrical systems, mixed-type differential equations, optimization, gradient, solving algorithm.