AN APPROACH FOR SIMULTANEOUSLY DETERMINING THE OPTIMAL TRAJECTORY AND CONTROL OF A VIBRATING SHELL

In this article, for a two-dimensional wave control system, we are going to present a new combinational solution path. First, by considering all necessary conditions, the problem is represented in a variational format in which the trajectory is shown by a trigonometric series with the unknown coe cients. Then the problem is converted into a new one that the unknowns are the mentioned coe cients and a positive Radon measure. It is proved that the optimal solution is existed and it is also explained how the optimal pair would be identied from the results deduced by a nite linear programming problem simultaneously. Two numerical examples are also given.