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Abstract and Applied Analysis
Volume 2015, Article ID 428042, 6 pages
http://dx.doi.org/10.1155/2015/428042
Research Article

Pontryagin’s Maximum Principle for the Optimal Control Problems with Multipoint Boundary Conditions

1Institute of Mathematics and Mechanics of ANAS, 9 B. Vahabzadeh Street, 1141 Baku, Azerbaijan
2Institute of Control Systems of ANAS, 9 B. Vahabzadeh Street, 1141 Baku, Azerbaijan
3Baku State University, 23 Z. Khalilov Street, 1148 Baku, Azerbaijan

Received 5 August 2014; Revised 29 September 2014; Accepted 30 September 2014

Academic Editor: Allaberen Ashyralyev

Copyright © 2015 M. J. Mardanov and Y. A. Sharifov. 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

Optimal control problem with multipoint boundary conditions is considered. Sufficient conditions for the existence and uniqueness of the solution of boundary value problem for every fixed admissible control are obtained. First order increment formula for the functional is derived. Pontryagin’s maximum principle is proved by using the variations of admissible control.