An Integro-Differential Approach to LQ-Optimal Control Problems for Heat Transfer in a Cylindrical Body

Optimal boundary control problems with linear-quadratic cost functions are considered for heat transfer processes in a cylindrical body. The method of integro-differential relations is used to reduce the original PDE model to a finite-dimensional controlled system. Three types of linear-quadratic cost functions are studied: the first includes control functions and terminal temperature distribution, the second additionally takes into account the heat flux at the terminal time instant and the third contains a measure of approximation error. Numerical examples are given and discussed.