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Erschienen in: Dynamic Games and Applications 3/2019

07.02.2019

Simultaneous Multiple Capture of Rigidly Coordinated Evaders

verfasst von: Aleksandr I. Blagodatskikh, Nikolai N. Petrov

Erschienen in: Dynamic Games and Applications | Ausgabe 3/2019

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Abstract

Differential games of two players represent a very serious mathematical theory. Conflict-controlled processes with many objects (at least from one of the opposing sides) are a natural generalization of differential games of two players. Mathematical problems involving the conflict interaction between two groups of controlled objects are the most difficult to investigate. The specific nature of these problems requires new methods of research. The problem of pursuit of a group of rigidly coordinated evaders in a nonstationary conflict-controlled process with equal capabilities is examined. We say that a multiple capture in the problem of pursuit holds if a certain number of pursuers catch evaders possibly at different instants. In the nonstrict simultaneous multiple capture, there is a requirement of coinciding instants of capture. Simultaneous multiple capture means that the smallest instants of capture coincide. In this paper, sufficient and necessary conditions for simultaneous multiple capture of rigidly coordinated evaders are obtained for the case where pursuers use piecewise-program counterstrategies. Control of the pursuers which can guarantee simultaneous multiple capture not later than at a finite instant is constructed explicitly. A number of examples are considered.

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Literatur
2.
Zurück zum Zitat Alias IA, Ibragimov GI, Rakmanov A (2016) Evasion differential games of infinitely many evaders from infinitely many pursuers in Hilbert space. Dyn Games Appl 6(2):1–13MathSciNet Alias IA, Ibragimov GI, Rakmanov A (2016) Evasion differential games of infinitely many evaders from infinitely many pursuers in Hilbert space. Dyn Games Appl 6(2):1–13MathSciNet
4.
Zurück zum Zitat Blagodatskikh AI, Petrov NN (2009) Conflict interaction of groups of controlled objects. Udmurt State University, Izhevsk (in Russian) Blagodatskikh AI, Petrov NN (2009) Conflict interaction of groups of controlled objects. Udmurt State University, Izhevsk (in Russian)
5.
6.
Zurück zum Zitat Blagodatskikh AI (2016) Multiple capture of rigidly coordinated evaders. Bull Udmurt Univ Math Mech Comput Sci 26(1):46–57 (in Russian) MathSciNetMATH Blagodatskikh AI (2016) Multiple capture of rigidly coordinated evaders. Bull Udmurt Univ Math Mech Comput Sci 26(1):46–57 (in Russian) MathSciNetMATH
7.
Zurück zum Zitat Blaquiere A, Gerard F, Leitmann G (1969) Quantitative and qualitative differential games. Academic Press, New YorkMATH Blaquiere A, Gerard F, Leitmann G (1969) Quantitative and qualitative differential games. Academic Press, New YorkMATH
8.
Zurück zum Zitat Bopardikar SD, Suri S (2014) \(k\)-Capture in multiagent pursuit evasion, or the lion and hyenas. Theor Comput Sci 522:13–23MathSciNetCrossRefMATH Bopardikar SD, Suri S (2014) \(k\)-Capture in multiagent pursuit evasion, or the lion and hyenas. Theor Comput Sci 522:13–23MathSciNetCrossRefMATH
9.
Zurück zum Zitat Chikrii AA (1992) Conflict controlled processes. Naukova Dumka, Kiev (in Russian) Chikrii AA (1992) Conflict controlled processes. Naukova Dumka, Kiev (in Russian)
10.
Zurück zum Zitat Demidovich BP (1967) Lectures on the mathematical stability theory. Nauka, Moscow (in Russian) MATH Demidovich BP (1967) Lectures on the mathematical stability theory. Nauka, Moscow (in Russian) MATH
11.
Zurück zum Zitat Friedman A (1971) Differential games. Wiley, New YorkMATH Friedman A (1971) Differential games. Wiley, New YorkMATH
12.
Zurück zum Zitat Ganebny SA, Kumkov SS, Le Ménec S, Patsko VS (2012) Model problem in a line with two pursuers and one evader. Dyn Games Appl 2:228–257 Ganebny SA, Kumkov SS, Le Ménec S, Patsko VS (2012) Model problem in a line with two pursuers and one evader. Dyn Games Appl 2:228–257
13.
Zurück zum Zitat Grigorenko NL (1990) Mathematical methods of control over multiple dynamic processes. Moscow State University, Moscow (in Russian) Grigorenko NL (1990) Mathematical methods of control over multiple dynamic processes. Moscow State University, Moscow (in Russian)
14.
15.
Zurück zum Zitat Hajek O (1975) Pursuit games. Academic Press, New YorkMATH Hajek O (1975) Pursuit games. Academic Press, New YorkMATH
16.
Zurück zum Zitat Huang H, Zhang W, Ding J, Stipanovic DM, Tomlin CJ (2011) Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers. In: Proceedings of the IEEE conference on decision and control. pp 4835–4840 Huang H, Zhang W, Ding J, Stipanovic DM, Tomlin CJ (2011) Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers. In: Proceedings of the IEEE conference on decision and control. pp 4835–4840
17.
Zurück zum Zitat Isaacs R (1965) Differential games: a mathematical theory with applications to warfare and pursuit, control and optimization. Wiley, New YorkMATH Isaacs R (1965) Differential games: a mathematical theory with applications to warfare and pursuit, control and optimization. Wiley, New YorkMATH
18.
Zurück zum Zitat Krasovskii NN, Subbotin AI (1974) Positional differential games. Nauka, Moscow (in Russian) MATH Krasovskii NN, Subbotin AI (1974) Positional differential games. Nauka, Moscow (in Russian) MATH
19.
Zurück zum Zitat Kuchkarov AS, Ibragimov GI, Khakestari M (2013) On a linear differential game of optimal approach of many pursuers with one evader. J Dyn Control Syst 19(1):1–15MathSciNetCrossRefMATH Kuchkarov AS, Ibragimov GI, Khakestari M (2013) On a linear differential game of optimal approach of many pursuers with one evader. J Dyn Control Syst 19(1):1–15MathSciNetCrossRefMATH
20.
Zurück zum Zitat Leitmann G (1974) Cooperative and non-cooperative many player differential games. Springer, ViennaCrossRefMATH Leitmann G (1974) Cooperative and non-cooperative many player differential games. Springer, ViennaCrossRefMATH
21.
Zurück zum Zitat Petrosyan LA (1977) Differential games of pursuit. Leningrad State University, Leningrad (in Russian) MATH Petrosyan LA (1977) Differential games of pursuit. Leningrad State University, Leningrad (in Russian) MATH
22.
Zurück zum Zitat Petrov NN (1997) Multiple capture in Pontryagin’s example with phase constraints. J Appl Math Mech 61(5):725–732MathSciNetCrossRef Petrov NN (1997) Multiple capture in Pontryagin’s example with phase constraints. J Appl Math Mech 61(5):725–732MathSciNetCrossRef
23.
Zurück zum Zitat Pontryagin LS (1971) A linear differential evasion game. Proc Steklov Inst Math 112:27–60 (in Russian) MathSciNetMATH Pontryagin LS (1971) A linear differential evasion game. Proc Steklov Inst Math 112:27–60 (in Russian) MathSciNetMATH
24.
Zurück zum Zitat Pshenichnyi BN (1976) Simple pursuit by several objects. Kibernetika 3:145–146MathSciNet Pshenichnyi BN (1976) Simple pursuit by several objects. Kibernetika 3:145–146MathSciNet
25.
Zurück zum Zitat Satimov N, Mamatov MS (1983) On problems of pursuit and evasion away from meeting in differential games between the group of pursuers and evaders. Doklady Akademii Nauk Uzbekskoj SSR 4:3–6 (in Russian) MATH Satimov N, Mamatov MS (1983) On problems of pursuit and evasion away from meeting in differential games between the group of pursuers and evaders. Doklady Akademii Nauk Uzbekskoj SSR 4:3–6 (in Russian) MATH
26.
Zurück zum Zitat Stipanovic DM, Melikyan A, Hovakimyan N (2010) Guaranteed strategies for nonlinear multi-player pursuit-evasion games. Int Game Theory Rev 12(1):1–17MathSciNetCrossRefMATH Stipanovic DM, Melikyan A, Hovakimyan N (2010) Guaranteed strategies for nonlinear multi-player pursuit-evasion games. Int Game Theory Rev 12(1):1–17MathSciNetCrossRefMATH
Metadaten
Titel
Simultaneous Multiple Capture of Rigidly Coordinated Evaders
verfasst von
Aleksandr I. Blagodatskikh
Nikolai N. Petrov
Publikationsdatum
07.02.2019
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 3/2019
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-019-00300-8

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