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Differential Games with the Langenhop Type Constrains on Controls

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Abstract

In 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 (\(\Pi\)-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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ACKNOWLEDGMENTS

We wish to thank A.A. Azamov and Sh.A. Alimov for discussing this paper and for providing some useful comments.

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Authors and Affiliations

  1. V.I. Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences and Namangan State University, Namangan, Uzbekistan

    B. T. Samatov

  2. Namangan State University, Namangan, Uzbekistan

    N. T. Umaraliyeva & S. I. Uralova

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  1. B. T. Samatov
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  2. N. T. Umaraliyeva
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  3. S. I. Uralova
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Correspondence to B. T. Samatov, N. T. Umaraliyeva or S. I. Uralova.

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(Submitted by T. K. Yuldashev)

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Samatov, B.T., Umaraliyeva, N.T. & Uralova, S.I. Differential Games with the Langenhop Type Constrains on Controls. Lobachevskii J Math 42, 2942–2951 (2021). https://doi.org/10.1134/S1995080221120295

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