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Bibliographic description:
Alekberov A. A.
AN ANALOG OF THE EULER EQUATION AND NECESSARY OPTIMALITY CONDITIONS OF THE SECOND ORDER IN ONE OPTIMAL CONTROL PROBLEM WITH VARIABLE STRUCTURE // BSU bulletin. Mathematics, Informatics. - 2019. №4. . - С. 12-30.
Title:
AN ANALOG OF THE EULER EQUATION AND NECESSARY OPTIMALITY CONDITIONS OF THE SECOND ORDER IN ONE OPTIMAL CONTROL PROBLEM WITH VARIABLE STRUCTURE
Financing:
Codes:
DOI: 10.18101/2304-5728-2019-4-12-30UDK: 517.977.52
Annotation:
The article considers an optimal control problem with variable structure, described by a combination of differential and integral equations, as well as by a performance functional of terminal type. Control fields are open. We have proved implicit necessary optimality conditions of the first and second orders. An analog of the Euler equation and an analog of Legendre–Clebsch condition are proved on the basis of studying nec- essary optimality conditions. The obtained new sequences of multipoint necessary con- ditions for the optimality of classical singular controls allow us to narrow down the set of admissible controls suspicious for optimality.
Keywords:
one-dimensional Volterra integral equation of the second kind; ordinary differential equation; necessary optimality condition; variation of the performance functional; Euler equation.
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