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Dynamic Games and Applications
Erschienen in: Dynamic Games and Applications 4/2017

16.11.2016

Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications

verfasst von: Sergey S. Kumkov, Stéphane Le Ménec, Valerii S. Patsko

Erschienen in: Dynamic Games and Applications | Ausgabe 4/2017

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Abstract

If a pursuit game with many persons can be formalized in the framework of zero-sum differential games, then general methods can be applied to solve it. But difficulties arise connected with very high dimension of the phase vector when there are too many objects. Just due to this problem, special formulations and methods have been elaborated for conflict interaction of groups of objects. This paper is a survey of publications and results on group pursuit games.
Vorheriger Artikel Aircraft Control During Cruise Flight in Windshear Conditions: Viability Approach
Nächster Artikel Erratum to: Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications

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Literatur
1.
Abramyants TG, Ivanov MN, Maslov EP, Yakhno VP (2004) A detection evasion problem. Autom Rem Control 65(10):1523–1530CrossRefMATH
2.
Abramyants TG, Maslov EP, Rubinovich EY (1980) An elementary differential game of alternative pursuit. Autom Rem Control 40(8):1043–1052MATH
3.
Abramyants TG, Maslov EP, Yakhno VP (2007) Evasion from detection in the three-dimensional space. J Comput Syst Sci Int 46(5):675–680MathSciNetCrossRefMATH
4.
Bakolas E, Tsiotras P (2010) On the relay pursuit of a maneuvering target by a group of pursuers. In: 50th IEEE conference on decision and control and European control conference (CDC-ECC’2011). IEEE, pp 7431–7436
5.
Bakolas E, Tsiotras P (2011) Optimal pursuit of moving targets using dynamic Voronoi diagrams. In: 49th IEEE conference on decision and control (CDC’2010). IEEE, pp 4270–4275
6.
Bardi M, Falcone M, Soravia P (1999) Numerical methods for pursuit-evasion games via viscosity solutions. In: Bardi M, Parthasaraty T, Raghavan TES (eds) Annals of the international society of dynamic games, vol 4. Birkhauser, Boston, pp 105–175
7.
Blagodatskih AI, Petrov NN (2009) Conflict interaction controlled objects groups. Udmurt State University, Izhevsk (in Russian)
8.
9.
Botkin ND, Hoffmann KH, Turova VL (2011) Stable numerical schemes for solving Hamilton–Jacobi–Bellman–Isaacs equations. SIAM J Sci Comput 33(2):992–1007MathSciNetCrossRefMATH
10.
Botkin ND, Ryazantseva EA (1992) Algorithm of constructing the solvability set for linear differential games of high dimension. Trudy Inst Mat i Mekh 2:128–134 (in Russian)MATH
11.
12.
Bryson AE, Ho YC (1975) Applied optimal control. Optimization, estimation and control. Hemisphere Publishing Corporation, Washington, DC
13.
Chen M, Fisac J, Sastry S, Tomlin C (2015) Safe sequential path planning of multi-vehicle systems via double-obstacle Hamilton–Jacobi–Isaacs variational inequality. In: Proceedings of the 14th European control conference, pp 3304–3309
14.
15.
Chikrii AA (1978) On the evasion problem in a linear differential game. Autom Rem Control 38(9):1291–1295
16.
Chikrii AA (1992) Conflict controlled processes. Naukova dumka, Kiev (in Russian)MATH
17.
Chikrii AA (1997) Conflict-controlled processes, mathematics and its applications, vol 405. Kluwer, DordrechtCrossRefMATH
18.
Dvurechensky PE, Ivanov GE (2014) Algorithms for computing Minkowski operators and their application in differential games. Comput Math Math Phys 54(2):235–264MathSciNetCrossRefMATH
19.
Fisac JF, Sastry S (2015) The pursuit-evasion-defense differential game in dynamic constrained environments. In: Proceedings of the IEEE 54th annual conference on decision and control (CDC), pp 4549–4556
20.
Ganebny SA, Kumkov SS, Le Ménec S, Patsko VS (2012) Model problem in a line with two pursuers and one evader. Dyn Games Appl 2:228–257MathSciNetCrossRefMATH
21.
Grigorenko NL (1989) On a quasilinear problem of pursuit by several objects. Sov Math Dokl 20:1365–1368MATH
22.
Grigorenko NL (1989) The pursuit problem in \(n\)-person differential games. Math USSR-Sb 63(1):35–45CrossRefMATH
23.
Grigorenko NL (1990) Mathematical methods of control of multiple dynamic processes. Moscow State University, Moscow (in Russian)
24.
Grigorenko NL, Kiselev YN, Lagunova NV, Silin DB, Trin’ko NG (1996) Solution methods for differential games. Comput Math Model 7(1):101–116MathSciNetCrossRefMATH
25.
26.
27.
Krasovskii NN, Subbotin AI (1974) Positional differential games. Nauka, Moscow (in Russian)MATH
28.
Krasovskii NN, Subbotin AI (1988) Game-theoretical control problems. Springer, New YorkCrossRef
29.
Kumkov SS, Le Ménec S, Patsko VS (2013) Model formulation of pursuit problem with two pursuers and one evader. In: Advances in aerospace guidance, navigation and control. Springer, Berlin, Heidelberg, pp 121–137
30.
Kumkov SS, Le Ménec S, Patsko VS (2014) Level sets of the value function in differential games with two pursuers and one evader. Interval analysis interpretation. Math Comput Sci 8:443–454MathSciNetCrossRefMATH
31.
Kumkov SS, Patsko VS (2001) Construction of singular surfaces in linear differential games. In: Altman E, Pourtallier O (eds) Annals of the international society of dynamic games: advances in dynamic games and applications, vol 6. Birkhauser, Boston, pp 185–202CrossRef
32.
Kumkov SS, Patsko VS, Shinar J (2005) On level sets with “narrow” throats in linear differential games. IGTR 7(3):285–312MathSciNetMATH
33.
Kurzhanski AB (2015) On a team control problem under obstacles. Proc Steklov Inst Math 291:128–142CrossRef
34.
Kurzhanski AB (2016) Problem of collision avoidance for a team motion with obstacles. Proc Steklov Inst Math 293:120–136CrossRefMATH
35.
Levchenkov AY, Pashkov AG (1990) Differential game of optimal approach of two inertial pursuers to a noninertial evader. JOTA 65(3):501–518MathSciNetCrossRefMATH
36.
Le Ménec S (2011) Linear differential game with two pursuers and one evader. In: Breton M, Szajowski K (eds) Annals of the international society of dynamic games, vol 11. Birkhauser, Boston, pp 209–226CrossRef
37.
Mikhalev DK, Ushakov VN (2007) Two algorithms for approximate construction of the set of positional absorption in the game problem of pursuit. Autom Rem Control 68(11):2056–2070CrossRefMATH
38.
Mishchenko EF, Nikol’skii MS, Satimov NY (1980) The problem of avoiding encounter in \(n\)-person differential games. Proc Steklov Inst Math 143:111–136MATH
39.
Nikol’skii MS (1983) On the alternating integral of Pontryagin. Sb Math 44(1):125–132CrossRef
40.
41.
Patsko VS, Turova VL (2001) Level sets of the value function in differential games with the homicidal chauffeur dynamics. IGTR 3(1):67–112MathSciNetMATH
42.
Petrosjan LA (1965) A family of differential survival games in the space \(R^{n}\). Sov Math Dokl 6:377–380
43.
Petrosyan LA (1966) The multi-person lifeline games of pursuit. Proc Armen Acad Sci Ser Math 1:331–340 (in Russian)
44.
Petrosyan LA (1977) Differential games of pursuit. Leningrad State University, Leningrad (in Russian)MATH
45.
Petrosyan LA (1993) Differential games of pursuit. World Scientific Publisher, LondonCrossRefMATH
46.
47.
48.
49.
50.
Polovinkin ES, Ivanov GE, Balashov MV, Konstantiov RV, Khorev AV (2001) An algorithm for the numerical solution of linear differential games. Sb Math 192(10):1515–1542MathSciNetCrossRefMATH
51.
Pontryagin LS (1967) Linear differential games, 1. Sov Math Dokl 8:769–771MATH
52.
Pontryagin LS (1967) Linear differential games, 2. Sov Math Dokl 8:910–912MATH
53.
54.
Pontryagin LS (1981) An algorithm for the numerical solution of linear differential games. Math USSR-Sb 40(3):285–303CrossRefMATH
55.
Pontryagin LS, Mishchenko EF (1969) A problem on the escape of one controlled object from another. Sov Math Dokl 10:1488–1490MATH
56.
Pschenichnyi BN (1976) Simple pursuit by several objects. Cybern Syst Anal 12(3):484–485MathSciNet
57.
Pschenichnyi BN, Chikrii AA, Rappoport IS (1981) An efficient method of solving differential games with many pursuers. Sov Math Dokl 23(1):104–109
58.
Pschenichnyi BN, Sagaidak MI (1970) Differential games of prescribed duration. Cybernetics 6(2):72–80CrossRef
59.
Rappoport IS, Chikrii AA (1997) Guaranteed result in a differential game of group pursuit with terminal payoff function. J Appl Math Mech 61(4):567–576MathSciNetCrossRef
60.
61.
62.
Shima T, Shinar J (2002) Time-varying linear pursuit-evasion game models with bounded controls. J Guid Control Dyn 25(3):425–432CrossRef
63.
Shinar J, Glizer VY, Turetsky V (2013) The effect of pursuer dynamics on the value of linear pursuit-evasion games with bounded controls. In: Krivan V, Zaccour G (eds) Annals of the international society of dynamic games, vol 13. Birkhauser, Boston, pp 313–350CrossRef
64.
Shinar J, Medinah M, Biton M (1984) Singular surfaces in a linear pursuit-evasion game with elliptical vectograms. JOTA 43(3):431–456MathSciNetCrossRefMATH
65.
Stipanović DM, Tomlin C, Leitmann G (2012) Monotone approximations of minimum and maximum functions and multi-objective problems. Appl Math Opt 66(3):455–473MathSciNetCrossRefMATH
66.
Subbotin AI (1995) Generalized solutions of first order PDEs. The dynamical optimization perspective. Birkhäuser, BostonCrossRefMATH
67.
Subbotin AI, Patsko VS (eds) (1984) Algorithms and programs for solving linear differential games. Institute of Mathematics and Mechanics, Ural Scientific Center, Academy of Sciences of USSR, Sverdlovsk (in Russian)
68.
Taras’ev AM, Ushakov VN, Khripunov AP (1988) On a computational algorithm for solving game control problems. J Appl Math Mech 51(2):167–172MathSciNetCrossRefMATH
69.
Ushakov VN (1981) On the problem of constructing stable bridges in a differential pursuit-evasion game. Eng Cybern 18(4):16–23
70.
Zarkh MA, Ivanov AG (1992) Construction of the value function in the linear differential game with the fixed terminal time. Trudy Inst Mat i Mekh 2:140–155 (in Russian)MATH
71.
Zarkh MA, Patsko VS (1988) Numerical solution of a third-order directed game. Eng Cybern 26(4):92–99MathSciNetMATH
Metadaten
Titel
Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications
verfasst von
Sergey S. Kumkov
Stéphane Le Ménec
Valerii S. Patsko
Publikationsdatum
16.11.2016
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 4/2017
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-016-0209-z

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