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Journal of Automation and Information Sciences

Published 12 issues per year

ISSN Print: 1064-2315

ISSN Online: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

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

Volume 45, Issue 8, 2013, pp. 59-67
DOI: 10.1615/JAutomatInfScien.v45.i8.60
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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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