First and second order necessary optimality conditions for a continuous stochastic control problem of Rosser type
R.O. Mastaliyev
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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 12 News of the Kabardino-Balkarian Scientific Center of RAS Vol. 27 No. 3 2025 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
For citation. Mastaliyev R.O. First and second order necessary optimality conditions for a continuous stochastic control problem of Rosser type. News of the Kabardino-Balkarian Scientific Center of RAS. 2025. Vol. 27. No. 3. Pp. 11–28. DOI: 10.35330/1991-6639-2025-27-3-11-28
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Information about the author
Rashad O. Mastaliyev, PhD Mathematics, Associate Professor, Head of the Department of Mathematic
and Informatic of the Azerbaijan University;
Az1007, Azerbaijan, Baku, 71 J. Hajibeyli street;
Leading Researcher at the Institute of Control Systems of the Ministry of Science and Education
of the Republic of Azerbaijan;
Az1141, Azerbaijan, Baku, 68 B. Vahabzade street;
mastaliyevrashad@gmail.com; rashad.mastaliyev@au.edu.az, ORCID: https://orcid.org/0000-0001-6387-2146
SPIN-code: 4056-5919