Optimum control of hyperbolic systems in the class of smooth control actions

The problem of optimal control of first order semi-linear hyperbolic equations system was studied. Control actions were selected from the class of smooth functions satisfying the integral constraints. We obtained the necessary optimality conditions of variational type in the class of admissible smooth controls. The condition of optimality was proved, and a scheme of iterative method was proposed. The numerical experiment was carried out in MATLAB 7.0 system. The results of numerical experiment showed that the proposed method of improving the smooth control functions could be effectively used to solve this class of problems.