{"id":3513,"date":"2025-08-06T13:20:34","date_gmt":"2025-08-06T12:20:34","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=3513"},"modified":"2026-04-13T10:02:43","modified_gmt":"2026-04-13T09:02:43","slug":"27-3-1-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-3-1-en\/","title":{"rendered":"27.3.1 En"},"content":{"rendered":"\n

First and second order necessary optimality conditions for a continuous stochastic control problem of Rosser type<\/strong><\/h1>\n\n\n\n

R.O. Mastaliyev<\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n\n\n\n

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Upload the full text<\/strong><\/strong><\/p>\n\n\n\n

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Abstract<\/strong>.<\/strong> <\/em>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<\/strong>. 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<\/strong>. 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.<\/p>\n\n\n\n

Keywords<\/strong>:<\/em><\/strong> Rosser-type stochastic system, Wiener random process, optimality, analogue of Euler equation, second-order optimality conditions<\/p>\n\n\n\n

For citation<\/strong>.<\/strong> 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<\/em>. 2025. Vol. 27. No. 3. Pp. 11\u201328. DOI: 10.35330\/1991-6639-2025-27-3-11-28<\/p>\n\n\n\n

R<\/strong>eferences<\/summary>\n
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  1. Mansimov K.B. On the theory of necessary optimality conditions in one problem with distributed parameters. Computational Mathematics and Mathematical Physics. 2001. Vol. 41. No. 10. Pp. 1429\u20131443. (In Russian)<\/li>\n\n\n\n
  2. Mansimov K.B. Study of quasi-singular processes in one problem of chemical reactor control. Differential equations. 1997. Vol. 33. No. 4. Pp. 544\u2013551. (In Russian)<\/li>\n\n\n\n
  3. Vasiliev O.V., Terletsky V.A. On the optimization of one class of controlled systems with distributed parameters. Optimization of dynamic systems. Minsk.1978. Pp. 26-30. (In Russian)<\/li>\n\n\n\n
  4. Mansimov K.B., Mastaliev R.O. Necessary conditions for first-order optimality in one stochastic control problem with distributed parameters. VSPU\/IPU RAS. 2024. Pp. 547\u2013549. (In Russian)<\/li>\n\n\n\n
  5. Mansimov K.B., Mastaliyev R.O. Analog of Euler equation and second order necessary optimality conditions for Rosser type continuous stochastic control problem. COIA-2024. 27\u201329 august. Istanbul. Turkiye. Pp. 567\u2013570.<\/li>\n\n\n\n
  6. Gabasov R., Kirillova F.M. Osobyye optimal’nyye upravleniya [Singular optimal controls]. Moscow: URSS, 2018. 256 p. (In Russian)<\/li>\n\n\n\n
  7. Mansimov K.B., Mardanov M.J. Kachestvennaya teoriya optimal’nogo upravleniya sistemami Gursa\u2013Darbu [Qualitative theory of optimal control of Goursat-Darboux systems]. Baku: Elm, 2010. 360 p. (In Russian)<\/li>\n\n\n\n
  8. Lu Q., Zhang X. Control theory for stochastic distributed parameters systems an engineering perspective. Annual Reviews in Control. 2021.Vol. 51. No. 6. Pp. 268\u2013330. DOI: 10.1016\/j.arcontrol.2021.04.002<\/li>\n\n\n\n
  9. Rachinsky V.V. Vvedeniye v obshchuyu teoriyu dinamiki sorbtsii i khromatografii [Introduction to the General Theory of Sorption and Chromatography Dynamics]. Moscow: Nauka, 1964. 136 p. (In Russian)<\/li>\n\n\n\n
  10. Khrychev D.A. On one stochastic quasilinear hyperbolic equation. Sbornik: Mathematics. Vol. 116(158). No. 3(11). Pp. 398\u2013426. DOI: 10.1070\/SM1983v044n03ABEH000972. (In Russian)<\/li>\n\n\n\n
  11. Vas’kovsky M.M. On solutions of stochastic hyperbolic equations with delay with measurable locally bounded coefficients. Bulletin of BSU. Series 1. Physics, Mathematics, Informatics. 2012. No. 2. Pp. 115\u2013121. EDN: RUPPAR. (In Russian)<\/li>\n\n\n\n
  12. Mansimov K.B., Mastaliev R.O. On the representation of the solution of the Goursat boundary value problem for stochastic hyperbolic partial differential equations of the first order. Bulletin of the Irkutsk State University, series. Mathematics. 2023. Vol. 45. Pp. 145\u2013151. DOI: 10.26516\/1997-7670.2023.45.145. (In Russian)<\/li>\n\n\n\n
  13. Mastaliev R.O. Necessary conditions for first-order optimality in stochastic Goursat \u2013 Darboux systems. Far Eastern Mathematical Journal. 2021. Vol. 21. No. 1. Pp. 89\u2013104. DOI: 10.47910\/FEMJ202108. (In Russian)<\/li>\n\n\n\n
  14. Mansimov K.B., Kerimova A.V. Necessary optimality conditions of the first and second orders in one step control problem described by difference and integro-differential equations of Volterra type. Computational Mathematics and Mathematical Physics. 2024. Vol. 64. No. 10. Pp. 2256\u20132268. DOI: 10.31857\/S0044466924100072. (In Russian)<\/li>\n\n\n\n
  15. Rzaeva V.G. Necessary optimality conditions of the first and second orders in one optimal control problem described by a system of hyperbolic integro-differential equations of the Volterra type. Bulletin of Tomsk State University. Management, Computer Science and Information Science. 2023. No. 62. Pp. 4\u201312. DOI: 10.17223\/19988605\/62\/1. (In Russian)<\/li>\n\n\n\n
  16. Butoma A.M., Sotskaya L.I. Variatsionnoye ischisleniye i optimal’noye upravleniye [Variational Calculus and Optimal Control]. Mogilev: Belarusian-Russian University, 2021. 46 p. (In Russian)<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong><\/summary>\n
    \n

    Rashad O. Mastaliyev<\/strong>, 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<\/p>\n\n\n\n

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    First and second order necessary optimality conditions for a continuous stochastic control problem of Rosser type R.O. Mastaliyev Upload the full text 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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-3513","page","type-page","status-publish","hentry"],"yoast_head":"\n27.3.1 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-3-1-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"27.3.1 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"First and second order necessary optimality conditions for a continuous stochastic control problem of Rosser type R.O. 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Mastaliyev Upload the full text 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 […]","og_url":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-3-1-en\/","og_site_name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","article_modified_time":"2026-04-13T09:02:43+00:00","twitter_card":"summary_large_image","twitter_misc":{"\u041f\u0440\u0438\u043c\u0435\u0440\u043d\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u0434\u043b\u044f \u0447\u0442\u0435\u043d\u0438\u044f":"5 \u043c\u0438\u043d\u0443\u0442"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-3-1-en\/","url":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-3-1-en\/","name":"27.3.1 En - 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