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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 156541, 12 pages
http://dx.doi.org/10.1155/2012/156541
Research Article

On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System

Department of Mathematics, Faculty of Science, Atatürk University, 25240 Erzurum, Turkey

Received 7 March 2012; Accepted 12 June 2012

Academic Editor: Valery Covachev

Copyright © 2012 Yeşim Saraç and Murat Subaşı. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use the initial condition on the state variable of a hyperbolic problem as control function and formulate a control problem whose solution implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and given targets. We prove the existence and the uniqueness of the optimal solution and establish the optimality condition. An iterative algorithm is constructed to compute the required optimal control as limit of a suitable subsequence of controls. An iterative procedure is implemented and used to numerically solve some test problems.