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自动化与信息科学期刊
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN 打印: 1064-2315
ISSN 在线: 2163-9337

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自动化与信息科学期刊

DOI: 10.1615/JAutomatInfScien.v45.i8.60
pages 59-67

Necessary Conditions of the Optimality of the Second Order in Optimal Control Problems Described by the System of Integrodifferential Equations of the Volterra Type

Kamil Bayramali oglu Mansimov
Institute of Cybernetics of National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
Misir Jumayil oglu Mardanov
Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Baku (Azerbaijan)

ABSTRACT

An optimal control problem, described by the system of integrodifferential equations of the Volterra type, is considered. Under the assumption of the openness of the controlled field the necessary optimality condition in the form of the Euler equation is derived. Further by examining the second variation of the performance criterion, different necessary conditions of the optimality of the second order have been found, expressed thought the parameters of the posed problem. In particular, the case of degeneration of the analogue of the Legendre−Clebsch condition has been studied. The multi-point necessary optimality conditions of special, in the classical sense, controls were proved.


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