## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2012, Special Issue (2012), Article ID 156541, 12 pages.

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

#### 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.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 156541, 12 pages.

**Dates**

First available in Project Euclid: 5 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1365174057

**Digital Object Identifier**

doi:10.1155/2012/156541

**Mathematical Reviews number (MathSciNet)**

MR2955024

**Zentralblatt MATH identifier**

1248.49009

#### Citation

Saraç, Yeşim; Subaşı, Murat. On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 156541, 12 pages. doi:10.1155/2012/156541. https://projecteuclid.org/euclid.aaa/1365174057