MATHEMATICS

To the necessary optimality conditions in one two-stage control problem for integro-differential equations of Volterra type

K. B. Mansimov^ab, A. F. Mansimzade<sup>a

a</sup> Baku State University
^b Institute of Control Systems of the Ministry of Science and Education of Azerbaijan, Baku

Abstract: The paper considers one two-stage optimal control problem, described at different time intervals by various integro-differential equations of the Volterra type. Under different assumptions two types of formulas for the increment of the quality functional are constructed for these problems. Studying them on various control variations, the analogues of the maximum principle of L.S. Pontryagin and the linearized maximum condition are proved.

Keywords: two-stage control problem, integro-differential equation, increment formula, admissible control, necessary optimality condition, optimal control.

UDC: 517.934

Received: 28.12.2023

DOI: 10.54341/20778708_2024_2_59_84