Electron. J. Diff. Equ., Vol. 2013 (2013), No. 80, pp. 1-11.

Optimal control problems for impulsive systems with integral boundary conditions

Allaberen Ashyralyev, Yagub A. Sharifov

In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.

Submitted February 2, 2013. Published March 22, 2013.
Math Subject Classifications: 34B10, 34A37, 34H05.
Key Words: Nonlocal boundary conditions; impulsive systems; optimal control problem.

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Allaberen Ashyralyev
Department of Mathematics, Fatih University
34500 Buyukcekmece, Istanbul, Turkey.
ITTU, Ashgabat, Turkmenistan.
email: aashyr@fatih.edu.tr
Yagub A. Sharifov
Baku State University, Institute of Cybernetics of ANAS
Baku, Azerbaijan
email: sharifov22@rambler.ru

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