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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 681862, 6 pages
http://dx.doi.org/10.1155/2013/681862
Research Article

Optimal Control Problem for Switched System with the Nonsmooth Cost Functional

1Department of Mathematics, Yasar University, 35100 İzmir, Turkey
2Department of Business Administration, Cologne University, 50931 Cologne, Germany

Received 2 July 2013; Revised 15 August 2013; Accepted 3 September 2013

Academic Editor: Nazim Idrisoglu Mahmudov

Copyright © 2013 Shahlar Meherrem and Rufan Akbarov. 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 examine the relationships between lower exhausters, quasidifferentiability (in the Demyanov and Rubinov sense), and optimal control for switching systems. Firstly, we get necessary optimality condition for the optimal control problem for switching system in terms of lower exhausters. Then, by using relationships between lower exhausters and quasidifferentiability, we obtain necessary optimality condition in the case that the minimization functional satisfies quasidifferentiability condition.