Optimal control over the process of heating of a thin core - Kopets, M.M. (Reports of the National Academy of Sciences of Ukraine, 2014)
The paper is devoted to the linear-quadratic optimal control problem for the process of heating of a thin core. The simultaneous use of distributed and boundary controls is supposed. A method of Lagrange multipliers is proposed, and the Lagrange function includes not only a partial differential equation, but also boundary conditions. For the considered optimization problem, the necessary conditions of optimality are obtained. Their analysis has given chance to deduce the Riccati integro-differential equation.