Abstract
An algorithm for numerical constructing level sets of the value function is shortly described for one class of linear differential games with fixed termination instant. Some model interception problems with one target and two interceptors are considered; all objects are weak maneuverable.
Similar content being viewed by others
References
Shima T.: Capture conditions in a pursuit-evasion game between players with biproper dynamics. JOTA 126(3), 503–528 (2005)
Shima T., Golan O.M.: Bounded differential games guidance law for dual-controlled missiles. IEEE Trans. Contr. Syst. Tech. 14(4), 719–724 (2006)
Shinar, J., Glizer, V.Y., Turetsky, V.: 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. Advances in Dynamic Games, vol. 13, pp 313–350. Birkhäuser, Boston (2013)
Shinar J., Medinah M., Biton M.: Singular surfaces in a linear pursuit-evasion game with elliptical vectograms. JOTA 43(3), 431–456 (1984)
Shima T., Shinar J.: Time-varying linear pursuit-evasion game models with bounded controls. J. Guid. Contr. Dyn. 25(3), 425–432 (2002)
Bryson A.E., Ho Y.-C: Applied optimal control, optimization, estimation and control. Hemisphere publishing corporation. Wiley, New York (1975)
Krasovskii, N.N., Subbotin, A.I.: Positional differential games. Nauka, Moscow (1974) (in Russian)
Krasovskii N.N., Subbotin A.I.: Game-theoretical control problems. Springer, New York (1988)
Pontryagin L.S.: Linear differential games. 2. Soviet Math. Dokl. 8, 910–912 (1967)
Pontryagin L.S.: Linear differential games of pursuit. Math. USSR Sb. 112(3), 307–330 (1980)
Nikol’skii M.S.: On the alternating integral of Pontryagin. Math. USSR Sb. 44(1), 125–132 (1983)
Nikol’skii M.S.: On the lower alternating integral of Pontryagin in linear differential games of pursuit. Math. USSR Sb. 128(1), 35–49 (1985)
Jaulin L., Kieffer M., Didrit O., Walter E.: Applied interval analysis. Springer, Berlin (2001)
Hansen E., Walster G.W.: Global optimization using interval analysis. 2nd edn. Dekker, New York (2004)
Ganebny S.A., Kumkov S.S., Le Ménec S., Patsko V.S.: Model problem in a line with two pursuers and one evader. Dyn. Games Appl. 2, 228–257 (2012)
Ganebny, S.A., Kumkov, S.S., Le Ménec, S., Patsko, V.S.: Study of linear game with two pursuers and one evader: different strength of pursuers. In: Cardaliaguet, P., Cressman, R. (eds.) Annals of the International Society of Dynamic Games. Advances in Dynamic Games, vol. 12, pp 269–292. Birkhäuser, Boston (2012)
Author information
Authors and Affiliations
Corresponding author
Additional information
The work is supported by the Russian Foundation for Basic Research (projects Nos. 12-01-00537 and 13-01-96055) and by the Program “Dynamic systems and control theory” of the Presidium of the RAS (project No.12-Π-1-1002).
Rights and permissions
About this article
Cite this article
Kumkov, S.S., Le Ménec, S. & Patsko, V.S. Level Sets of the Value Function in Differential Games with Two Pursuers and One Evader. Interval Analysis Interpretation. Math.Comput.Sci. 8, 443–454 (2014). https://doi.org/10.1007/s11786-014-0203-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11786-014-0203-z
Keywords
- Group differential pursuit-evasion games
- Linear dynamics
- Value function
- Level sets
- Numerical construction