This article is cited in 7 papers

Differential Equations

Optimal control problem for the impulsive differential equations with non-local boundary conditions

Ya. A. Sharifov<sup>ab

a</sup> Baku State University, Baku, AZ-1073/1, Azerbaijan
^b Institute of Cybernetics named after Academician A. Huseynov, National Academy of Sciences of Aserbaijan, Baku, AZ1141, Azerbaijan

Abstract: The optimal control problem is investigated, where the state of the controlled system is described by the impulsive differential equations with non-local boundary conditions. The existence and uniqueness of the non-local impulsive boundary problem by fixed admissible controls are proved using the contraction mapping principle. The gradient of the functional is calculated under certain conditions on the initial data. The necessary conditions for optimality of the first order are obtained.

Keywords: non-local boundary conditions, impulsive systems, necessary conditions of optimality, gradient of functional, existence and uniqueness of the solution.

UDC: 517.977.5

MSC: Primary 34B37; Secondary 49K15

Original article submitted 09/XI/2012
revision submitted – 21/IX/2013

DOI: 10.14498/vsgtu1134

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