Discrete and continuous optimal control strategies in the selective cooling of steel

We consider the problem of cooling milled steel profiles at a maximum rate subject to given bounds on the difference of temperatures in prescribed poi nts of the steel profile. This leads to a nonlinear parabolic control probl em with state constrains in a 2D domain. The controls can admit values from continuous or discrete sets. A method of instantaneous control is applied to establish a fast solution technique. Moreover, continuous and discrete c ontrol strategies are compared, and conclusions are given from an applicati onal point of view.