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Abstract and Applied Analysis
Volume 2013, Article ID 946910, 9 pages
Research Article

Maximum Principle in the Optimal Control Problems for Systems with Integral Boundary Conditions and Its Extension

1Meshkin Shahr Branch, Islamic Azad University, Meshkin Shahr 5661668691, Iran
2Baku State University, Z. Khalilov Street 23, 1148 Baku, Azerbaijan
3Institute Cybernetics of Azerbaijan National Academy of Sciences, B. Vahab-Zade Street 9, 1141 Baku, Azerbaijan

Received 19 April 2013; Revised 14 June 2013; Accepted 1 July 2013

Academic Editor: Nazim Idrisoglu Mahmudov

Copyright © 2013 A. R. Safari et al. 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.


The optimal control problem with integral boundary condition is considered. The sufficient condition is established for existence and uniqueness of the solution for a class of integral boundary value problems for fixed admissible controls. First-order necessary condition for optimality is obtained in the traditional form of the maximum principle. The second-order variations of the functional are calculated. Using the variations of the controls, various optimality conditions of second order are obtained.