Mathematics and Mechanics

First and second order necessary optimality conditions for a continuous stochastic control problem of Rosser type

R. O. Mastaliev<sup>ab

a</sup> Azerbaijan University, Az1007, Azerbaijan, Baku, 71 J. Hajibeyli street
^b Institute of Control Systems of the Ministry of Science and Education of the Republic of Azerbaijan, Az1141, Azerbaijan, Baku, 68 B. Vahabzade street

Abstract: This paper is devoted to the study of a singular, in the classical sense, case and the derivation second order necessary optimality conditions in terms of the second variation of the minimizable functional in the stochastic control problem described by first order stochastic nonlinear hyperbolic equations system written in the canonical form. Results. For one stochastic optimal control problem described by a stochastic system of first-order nonlinear hyperbolic equations, necessary conditions of first- and second-order optimality are obtained, which are, respectively, stochastic analogs of the Euler equation and optimality conditions for the classical extremal. Methods. In obtaining the results, theories of optimal control and calculus of variations were used, taking into account the stochastic properties of the problem under consideration. Similar control problems arise in the optimization of a number of chemical-technological processes under the influence of random effects.

Keywords: Rosser-type stochastic system, Wiener random process, optimality, analogue of Euler equation, second-order optimality conditions

UDC: 519.21:517.977.56

MSC: 93E20

Received: 27.03.2025
Revised: 28.04.2025
Accepted: 07.05.2025

DOI: 10.35330/1991-6639-2025-27-3-11-28

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