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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 5, Pages 86–92 (Mi ivm9116)  
This article is cited in 6 scientific papers (total in 6 papers)

Brief communications

Optimality conditions for extremal controls in bilinear and quadratic problems

V. A. Srochko, V. G. Antonik

Irkutsk State University, 1 K. Marks str., Irkutsk, 664003 Russia
Full-text PDF (154 kB) Citations (6)
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Abstract: We consider the problem of optimization of bilinear functional with respect to linear phase system and modular control constraint. We obtain sufficient conditions of optimality for extremal controls. They complement the maximum principle and preserve the complexity of its implementation. These conditions are presented in the form of inequalities for functions of one variable on the time interval. The optimization problem for quadratic functional is reduced to the bilinear case with the help of the adjoint matrix function.
Keywords: non-convex optimal control problems, the maximum principle, sufficient optimality conditions.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00564
Received: 25.11.2015
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 5, Pages 75–80
DOI: https://doi.org/10.3103/S1066369X1605008X
Bibliographic databases:
Document Type: Article
UDC: 517.97
Language: Russian
Citation: V. A. Srochko, V. G. Antonik, “Optimality conditions for extremal controls in bilinear and quadratic problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 5, 86–92; Russian Math. (Iz. VUZ), 60:5 (2016), 75–80
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/ivm9116
  • https://www.mathnet.ru/eng/ivm/y2016/i5/p86
    • This publication is cited in the following 6 articles:
    1. V. A. Srochko, A. V. Arguchintsev, “Parametricheskaya regulyarizatsiya funktsionala v lineino-kvadratichnoi zadache optimalnogo upravleniya”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 49 (2024), 32–44  mathnet  crossref
    2. A. V. Arguchintsev, V. P. Poplevko, “Variatsionnoe uslovie optimalnosti v zadache upravleniya lineinoi giperbolicheskoi sistemoi pervogo poryadka s zapazdyvaniem na granitse”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 212, VINITI RAN, M., 2022, 3–9  mathnet  crossref
    3. A. Arguchintsev, V. Poplevko, “An optimal control problem by a hybrid system of hyperbolic and ordinary differential equations”, Games, 12:1 (2021), 23  crossref  mathscinet  isi  scopus
    4. A V Arguchintsev, M S Kedrina, “Determination of functional parameters in boundary conditions of linear hyperbolic systems by optimal control methods”, J. Phys.: Conf. Ser., 1847:1 (2021), 012014  crossref
    5. V. G. Antonik, A. V. Arguchintsev, “To the 75th Anniversary of the Birth of Professor V. A. Srochko”, Bull. Irkutsk State Univ.-Ser. Math., 34 (2020), 126–134  crossref  mathscinet  zmath  isi
    6. O. V. Morzhin, “Nelokalnoe uluchshenie upravlenii v nelineinykh diskretnykh sistemakh”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 150–163  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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