Two weak pursuers in a game against a single evader (original) (raw)

References

1. Le Ménec, S., Linear Differential Game with Two Sursuers and One Evader, in Annals of the Int. Society of Dynamic Games, vol. 11: Advances in Dynamic Games. Theory, Applications, and Numerical Methods for Differential and Stochastic Games, Breton, M. and Szajowski, K., Eds., Boston: Birkhauser, 2011, pp. 209–226.
   Google Scholar
2. Ganebny, S.A., Kumkov, S.S., Le Ménec, S., et al., Model Problem in a Line with Two Pursuers and One Evader, Dyn. Games Appl., 2012, vol. 2, pp. 228–257.
   Article MathSciNet MATH Google Scholar
3. Ganebny, S.A., Kumkov, S.S., Le Ménec, S., et al., Study of Linear Game with Two Pursuers and One Evader: Different Strength of Pursuers, in Annals of the Int. Society of Dynamic Games, vol. 12: Advances in Dynamic Games, Cardaliaguet, P. and Cressman, R., Eds., Boston: Birkhauser, 2012, pp. 269–292.
   Google Scholar
4. Shinar, J. and Shima, T., Non-Orthodox Guidance Law Development Approach for Intercepting Maneuvering Targets, J. Guid. Control Dyn., 2002, vol. 25, no. 4, pp. 658–666.
   Article Google Scholar
5. Isaacs, R., Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control, and Optimization, New York: Wiley, 1965. Translated under the title Differentsial’nye igry, Moscow: Mir, 1967.
   MATH Google Scholar
6. Krasovskii, N.N. and Subbotin, A.I., Pozitsionnye differentsial’nye igry (Positional Differential Games), Moscow: Nauka, 1974.
   MATH Google Scholar
7. Krasovskii, N.N., Upravlenie dinamicheskoi sistemoi (Control of a Dyanmic System), Moscow: Nauka, 1985.
   Google Scholar
8. Krasovskii, N.N. and Subbotin, A.I., Game-Theoretical Control Problems, New York: Springer-Verlag, 1988.
   Book MATH Google Scholar
9. Taras’ev, A.M., Uspenskii, A.A., and Ushakov, V.N., Approximation Schemes and Finite-Difference Operators for Constructing Generalized Solutions of Hamilton-Jacobi Equations, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1994, no. 3, pp. 173–185.
   Google Scholar
10. Bardi, M. and Capuzzo-Dolcetta, I., Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Boston: Birkhauser, 1997.
    Book MATH Google Scholar
11. Botkin, N.D. and Patsko, B.C., Positional Control in a Linear Differential Game, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1983, no. 4, pp. 78–85.
    Google Scholar
12. Botkin, N.D., Kein, V.M., and Patsko, V.S., Model Problem of Controlling a Plane’s Side Motion During Landing, Prikl. Mat. Mekh., 1984, vol. 48, no. 4, pp. 560–567.
    Google Scholar
13. Patsko, V.S., Switching Surfaces in Linear Differential Games, Sovrem. Mat. Pril., 2005, vol. 23, pp. 79–122.
    Google Scholar
14. Pshenichnyi, B.N., Simple Pursuit by Several Objects, Kibernetika, 1976, no. 3, pp. 145–146.
    Google Scholar
15. Chikrii, A.A., Konfliktno upravlyaemye protsessy (Conflict Controlled Processes), Kiev: Naukova Dumka, 1992.
    Google Scholar
16. Grigorenko, N.L., Matematicheskie metody upravleniya neskol’kimi dinamicheskimi protsessami (Mathematical Methods for Control over Several Dynamic Processes), Moscow: Mosk. Gos. Univ., 1990.
    Google Scholar
17. Blagodatskikh, A.I. and Petrov, N.N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob”ektov (Conflict Interaction of Groups of Controllable Objects), Izhevsk: Udmurt. Univ., 2009.
    Google Scholar
18. Petrosyan, L.A., Differentsial’nye igry presledovaniya (Differential Pursuit Games), Leningrad: Leningr. Gos. Univ., 1977.
    Google Scholar
19. Petrosyan, L.A. and Tomskii, G.V., Geometriya prostogo presledovaniya (Geometry of Simple Pursuit), Novosibirsk: Nauka, 1983.
    MATH Google Scholar
20. Rikhsiev, B.B., Differentsial’nye igry s prostymi dvizheniyami (Differential Games with Simple Motions), Tashkent: Fan, 1989.
    MATH Google Scholar
21. Ol’shanskii, V.K. and Rubinovich, E.Ya., Elementary Differential Games of Pursuit of a Two-Object System, Autom. Remote Control, 1974, vol. 35, no. 1, part 1, pp. 19–28.
    MathSciNet Google Scholar
22. Hagedorn, P. and Breakwell, J.V., A Differential Game with Two Pursuers and One Evader, JOTA, 1976, vol. 18, no. 1, pp. 15–29.
    Article MathSciNet MATH Google Scholar
23. Melikyan, A.A., Optimal Interaction of Two Pursuers in a Game Problem, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1981, no. 2, pp. 49–56.
    Google Scholar
24. Pashkov, A.G. and Terekhov, S.D., A Differential Game of Approach with Two Pursuers and One Evader, JOTA, 1987, vol. 55, no. 2, pp. 303–312.
    Article MathSciNet MATH Google Scholar
25. Stipanović, D.M., Tomlin, C.J., and Leitmann, G., Monotone Approximations of Minimum and Maximum Functions and Multi-Objective Problems, Appl. Math. Optim., 2012, vol. 66, pp. 455–473.
    Article MathSciNet MATH Google Scholar
26. Shima, T. and Shinar, J., Time-Varying Linear Pursuit-Evasion Game Models with Bounded Controls, J. Guid. Control Dyn., 2002, vol. 25, no. 3, pp. 425–432.
    Article Google Scholar
27. Subbotin, A.I. and Chentsov, A.G., Optimizatsiya garantii v zadachakh upravleniya (Optimizing Guarantees in Control Problems), Moscow: Nauka, 1981.
    MATH Google Scholar

Download references