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Differential Games with the Langenhop Type Constrains on Controls

Authors
  • Samatov, B. T.1
  • Umaraliyeva, N. T.2
  • Uralova, S. I.2
  • 1 V.I. Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences and Namangan State University, Namangan, Uzbekistan , Namangan (Uzbekistan)
  • 2 Namangan State University, Namangan, Uzbekistan , Namangan (Uzbekistan)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Dec 13, 2021
Volume
42
Issue
12
Pages
2942–2951
Identifiers
DOI: 10.1134/S1995080221120295
Source
Springer Nature
Keywords
Disciplines
  • Article
License
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Abstract

AbstractIn this article, the concept of a Langenhop type constraint on the controls of players is introduced. The relationship between geometric, Langenhop and integral constraints is investigated. For these three classes, the attainability domains of the players are found by admissible controls. The parallel pursuit strategy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi$$\end{document}-strategy) is constructed for differential game of pursuit with Langenhop type constraints and the sufficient solvability conditions of the problem are obtained. To solve the evasion problem, the lower bounds of the convergence, depending on the given parameters, is found. This work develops the works of Isaacs, Petrosjan, Pshenichnyi, Azamov and other researchers, including the authors.

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