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Matematicheskie Zametki, 2019, Volume 106, Issue 3, Pages 409–423
DOI: https://doi.org/10.4213/mzm11975 (Mi mzm11975) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On the Theory of Optimal Processes in Discrete Systems

M. D. Mardanova, T. K. Melikovab, S. T. Melika

a Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences
b Institute of Control Systems, National Academy of Sciences of Azerbaijan
Full-text PDF (551 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm11975
Abstract: In this paper, by introducing the notion of $\gamma$-convex set, we isolate a wider class of discrete control systems in which the global maximum principle holds. A new type of variation of control for such classes of discrete control systems is proposed and stronger global maximum principle and second-order optimality condition expressed in terms of a singular control of new type are obtained. Generalizing the notion of the relative interior of sets, we obtain an optimality condition for discrete systems in the form of an equality, which we call Pontryagin's equation.
Keywords: discrete maximum principle, $\gamma$-convex set, optimality conditions of second order.
Received: 21.02.2018
English version:
Mathematical Notes, 2019, Volume 106, Issue 3, Pages 390–401
DOI: https://doi.org/10.1134/S0001434619090086
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: M. D. Mardanov, T. K. Melikov, S. T. Melik, “On the Theory of Optimal Processes in Discrete Systems”, Mat. Zametki, 106:3 (2019), 409–423; Math. Notes, 106:3 (2019), 390–401
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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