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Yayın A simultaneously determination of the optimal trajectory and control for vibrating shell systems by measures(Maltepe Üniversitesi, 2009) Sahebi, H. R.; Ebrahimi, S.; Fakharzadeh J., A.In the recent decade, a considerable number of optimal control problems have been solved successfully based on the properties of the measures. This method, called embedding method, has many useful benefits like finding the global solution, a linear treatment even for the strong nonlinear problems and also easy calculations in the numerical schemes. But, in general, the method is not able to determine the optimal trajectory and control at the same time; moreover, it rarely uses the advantages of the classical solutions of the involved systems. In this article, for a wave control system governed by vibrating shell equations, we are going to present a new solution path by applying this method and also using the trigonometric series. First by considering all conditions, the problem is represented in a variational format in which the trajectory is shown by a trigonometric series with the unknown coefficients. Then the problem is converted into a measure theoretical optimization one that the unknowns are the mentioned coefficients and a positive radon measure. It is also proved that the new problem has the optimal solution and how one be able to identify the optimal trajectory and control simultaneously form the solution of a finite linear programming problem. In this manner some numerical examples are also given.
