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Sbornik: Mathematics, 2005, Volume 196, Issue 4, Pages 513–539
DOI: https://doi.org/10.1070/SM2005v196n04ABEH000890 (Mi sm1284) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Construction of solutions in certain differential games with phase constraints

S. V. Grigor'evaa, V. Yu. Pakhotinskikhb, A. A. Uspenskiia, V. N. Ushakova

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural State Technical University
English version PDF (376 kB) Citations (21)
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DOI: https://doi.org/10.1070/SM2005v196n04ABEH000890
Abstract: A differential approach-evasion game with fixed termination time is studied. It is assumed that the phase vector of the conflict-control system is subjected to constraints that form a closed set in the position space. The ideology of stable bridges is used for solving the problem.
A method of convolution is proposed, which is used in several problems for constructing explicitly the stable absorption operator defining the stable bridges. A method of approximate construction of the maximal stable bridge in this game is suggested. The relations are written down that define a system of sets approximating the maximal stable bridge, and a control procedure with a guide is described, which can be used for obtaining an approximate solution of the approach problem.
Received: 05.05.2004
Russian version:
Matematicheskii Sbornik, 2005, Volume 196, Number 4, Pages 51–78
DOI: https://doi.org/10.4213/sm1284
Bibliographic databases:
UDC: 512
MSC: Primary 49N70; Secondary 49N75, 91A23
Language: English
Original paper language: Russian
Citation: S. V. Grigor'eva, V. Yu. Pakhotinskikh, A. A. Uspenskii, V. N. Ushakov, “Construction of solutions in certain differential games with phase constraints”, Mat. Sb., 196:4 (2005), 51–78; Sb. Math., 196:4 (2005), 513–539
Citation in format AMSBIB
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    • This publication is cited in the following 21 articles:
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