On the optimal control problem to solutions of one Granberg model

The active development of methods for solving inhomogeneous systems of differential equations with a degenerate matrix with a derivative is primarily associated with a wide range of applied problems. Optimal control to solutions of these problems is also an important area of research. The article considers the problem on optimal control to solutions of the non-stationary Granberg model. The main methods of the study are methods of the theory of degenerate (semi) groups and optimal control for Sobolev type equations. The given example of solving the problem from the monograph written by A.G. Granberg illustrates the advantages of the applied methods for solving. Namely, the methods do not require the introduction of assumptions that were applied earlier and do not correspond to real situations when solving such problems. Also, as an example, we give an exact solution to the optimal control problem in which the planned values of economic indicators are taken in the form of a second-order polynomial with a control action in the form of a third-order polynomial. In addition, we propose an algorithm for numerically solving the optimal control problem under consideration.