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 Trudy Inst. Mat. i Mekh. UrO RAN, 2017, Volume 23, Number 2, Pages 285–302 (Mi timm1430)

Stability iterations and an evasion problem with a constraint on the number of switchings

A. G. Chentsovab

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: For an approach-evasion differential game, we consider a variant of the method of program iterations called stability iterations. A connection is established between the iterative procedure and the solution of an evasion problem with a constraint on the number of switchings: the stability iterations define the successful solvability set of the problem. It is proved that the evasion is possible if and only if the strict evasion is possible (i.e., the evasion with respect to neighborhoods of sets defining the approach-evasion game). We specify a representation of the strategies that guarantee the evasion with a constraint on the number of switchings. These strategies are defined as triplets whose elements are a multidimensional positional control strategy, a correction strategy realized as a mapping that takes a game position to a nonanticipating multifunctional on the trajectory space and defines the choice of the switching times, and a positive integer that satisfies the constraints on the number of switchings and specifies the number of switchings of the control. It is important that we use nonanticipating multifunctionals as a tool for generating the controls of the evading player. The paper is in line with the research carried out by N.N.Krasovskii's school on control theory and the theory of differential games.

Keywords: nonanticipating multifunctional, stability operator, correction strategy.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-0050516-01-00649

DOI: https://doi.org/10.21538/0134-4889-2017-23-2-285-302

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Bibliographic databases:

UDC: 519.6
MSC: 49J15, 49K15, 93C15, 49N70

Citation: A. G. Chentsov, “Stability iterations and an evasion problem with a constraint on the number of switchings”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 2, 2017, 285–302

Citation in format AMSBIB
\Bibitem{Che17} \by A.~G.~Chentsov \paper Stability iterations and an evasion problem with a constraint on the number of switchings \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2017 \vol 23 \issue 2 \pages 285--302 \mathnet{http://mi.mathnet.ru/timm1430} \crossref{https://doi.org/10.21538/0134-4889-2017-23-2-285-302} \elib{https://elibrary.ru/item.asp?id=29295271} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. G. Chentsov, “Iteratsii stabilnosti i zadacha ukloneniya s ogranicheniem na chislo pereklyuchenii formiruemogo upravleniya”, Izv. IMI UdGU, 49 (2017), 17–54
2. A. G. Chentsov, D. M. Khachai, “Relaksatsiya differentsialnoi igry sblizheniya-ukloneniya i metody iteratsii”, Tr. IMM UrO RAN, 24, no. 4, 2018, 246–269
3. A. Chentsov, D. Khachay, “Towards a relaxation of the pursuit-evasion differential game”, IFAC PAPERSONLINE, 52:13 (2019), 2303–2307
4. A. G. Chentsov, D. M. Khachai, “Operator programmnogo pogloscheniya i relaksatsiya differentsialnoi igry sblizheniya–ukloneniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:1 (2020), 64–91
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