Numerical solution to the optimal feedback control of continuous casting process

Using a semi-discrete model that describes the heat transfer of a continuous casting process of steel, this paper is addressed to an optimal control problem of the continuous casting process in the secondary cooling zone with water spray control. The approach is based on the Hamilton-Jacobi-Bellman equation satisfied by the value function. It is shown that the value function is the viscosity solution of the Hamilton-Jacobi-Bellman equation. The optimal feedback control is found numerically by solving the associated Hamilton-Jacobi-Bellman equation through a designed finite difference scheme. The validity of the optimality of the obtained control is experimented numerically through comparisons with different admissible controls. Detailed study of a low-carbon billet caster is presented.