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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/timm1430
https://www.mathnet.ru/eng/timm/v23/i2/p285
This publication is cited in the following 11 articles:
A. G. Chentsov, “On the Relaxation of a Game Problem of Approach with Priority Elements”, Proc. Steklov Inst. Math. (Suppl.), 317, suppl. 1 (2022), S55–S70
A. G. Chentsov, “Guidance–Evasion Differential Game: Alternative Solvability and Relaxations of the Guidance Problem”, Proc. Steklov Inst. Math., 315 (2021), 270–289
A. G. Chentsov, “O svoistvakh odnogo funktsionala, ispolzuemogo v programmnykh konstruktsiyakh resheniya differentsialnykh igr”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:4 (2021), 668–696
A. G. Chentsov, “Differential approach-evasion game: alternative solvability and the construction of relaxations”, Differ. Equ., 57:8 (2021), 1088–1114
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
A. G. Chentsov, “Nekotorye voprosy teorii differentsialnykh igr s fazovymi ogranicheniyami”, Izv. IMI UdGU, 56 (2020), 138–184
A. G. Chentsov, D. M. Khachay, “Relaxation of a dynamic game of guidance and program constructions of control”, Minimax Theory Appl., 5:2, SI (2020), 275–304
A. Chentsov, D. Khachay, “Towards a relaxation of the pursuit-evasion differential game”, IFAC PAPERSONLINE, 52:13 (2019), 2303–2307
Alexander Chentsov, Daniel Khachay, Studies in Systems, Decision and Control, 203, Advanced Control Techniques in Complex Engineering Systems: Theory and Applications, 2019, 129
A. G. Chentsov, D. M. Khachai, “Relaxation of the Pursuit–Evasion Differential Game and Iterative Methods”, Proc. Steklov Inst. Math. (Suppl.), 308, suppl. 1 (2020), S35–S57
A. G. Chentsov, “Iteratsii stabilnosti i zadacha ukloneniya s ogranicheniem na chislo pereklyuchenii formiruemogo upravleniya”, Izv. IMI UdGU, 49 (2017), 17–54
Citation in format AMSBIB
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