Cybernetics And Systems Analysis logo
Editorial Board Announcements Abstracts Authors Archive
Cybernetics And Systems Analysis
International Theoretical Science Journal
Volume 55 >>> № 2 MARCH — APRIL 2019
UDC 517.977
J.S. Rappoport1


1 V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine

 jeffrappoport@gmail.com

STROBOSCOPIC STRATEGY IN GAME DYNAMIC PROBLEMS WITH TERMINAL
PAY OFF FUNCTION AND INTEGRAL CONSTRAINTS ON CONTROLS

Abstract. The paper considers linear differential games with a terminal payoff function and integral constraints on controls. Sufficient conditions for game completion in a finite guaranteed time in the class of quasi-strategies are formulated. Two schemes of the method of resolving functions are proposed that ensure game completion in a final guaranteed time in the class of stroboscopic strategies. It is shown that without additional assumptions, this time coincides with the guaranteed time in the class of quasistrategies.

Keywords: linear differential game, terminal payoff function, integral constraints, multivalued mapping, measurable selector, stroboscopic strategy.



FULL TEXT

REFERENCES

  1. Rappoport J.S., Chikriy A.A. On the guaranteed result in a differential game with a terminal payoff function. Prikladnaya Matematika i Mekhanika. 1995. Vol. 59, No. 5. P. 714–720.

  2. Rappoport J.S., Chikriy A.A. Guaranteed result in a differential group pursuit game with a terminal payoff function. Prikladnaya Matematika i Mekhanika. 1997. Vol. 61, No. 4. P. 584–594.

  3. Rappoport J.S. The method of resolving functions in the theory of conflict-controlled processes with a terminal payoff function. Problemy upravleniya i informatiki. 2016. No. 3. P. 49–58.

  4. Rappoport J.S. Stroboscopic strategy in the resolving-functions method for control game problems with terminal payoff function. Kibernetika i sistemnyj analiz. 2016. Vol. 52, No. 4. P. 90–102.

  5. Nikolsky M.S. Direct method in linear differential games with integral constraints. Upravlyayemyye sistemy. 1969. Iss. 2. P. 49–59.

  6. Chikriy A.A., Bezmagorychny V.V. The method of resolving functions in linear differential games with integral constraints. Avtomatika. 1993. No. 4. P. 26–36.

  7. Chikriy A.A., Belousov A.A. On linear differential games with integral convergence constraints. Tr. IMM UB RAS. 2009. Vol. 15, No. 4. P. 290–301.

  8. Samatov B.T. Problems of group pursuit with integral constraints on controls of players. I. Kibernetika i sistemnyj analiz. 2013. Vol. 49, No. 5. P. 132–145.

  9. Rappoport J.S. Resolving-functions method for game theory control problems with integral constraints. Kibernetika i sistemnyj analiz. 2018. Vol. 54, No. 5. P. 109–127.

  10. Chikrii A.A. Conflict controlled processes. Dordrecht; Boston; London: Springer Science and Business Media, 2013. 424 p.

  11. Chikriy A.A., Rappoport J.S. The method of resolving functions in the theory of conflict-controlled processes. Kibernetika i sistemnyj analiz. 2012. Vol. 48, No. 4. P. 40–64.

  12. Chikriy A.A., Chikriy V.K. The structure of images of multi-valued mappings in game motion control problems. Problemy upravleniya i informatiki. 2016. No. 3. P. 65–78.

  13. Rappoport J.S. Sufficient conditions for guaranteed results in a differential game with a terminal payoff function. Problemy upravleniya i informatiki. 2018. No. 1. P. 72–84.

  14. Hajek O. Pursuit games. New York: Academic Press, 1975. Vol. 12. 266 p.

  15. Krasovsky N.N., Subbotin A.I. Positional differential games [in Russian]. Moscow: Nauka, 1974. 455 p.

  16. Pontryagin L.S. Selected scientific works [in Russian]. Moscow: Nauka, 1988. Vol. 2. 576 p.

  17. Nikolsky M.S. The first direct method L.S. Pontryagin in differential games [in Russian]. Moscow: Moscow State University Publishing House, 1984. 65 p.

  18. Pittsyk M.V., Chikrii A.A. On a group pursuit problem. Journal of Applied Mathematics and Mechanics. 1982. Vol. 46, N 5. P. 584–589.

  19. Chikrii A.A., Kalashnikova S.F. Pursuit of a group of evaders by a single controlled object. Cybernetics. 1987. Vol. 23, N 4. P. 437–445.

  20. Chikrii A.A. Multivalued mappings and their selections in game control problems. Journal of Automation and Information Sciences. 1995. Vol. 27, N 1. P. 27–38.

  21. Chikriy A.A., Adelman S.D. Generalized Mittag-Leffler matrix functions in game problems for fractional-order evolution equations. Kibernetika i sistemnyj analiz. 2000. No. 3. С. 3–32.

  22. Albus J., Meystel A., Chikrii A.A., Belousov A.A., Kozlov A.J. Analytical method for solution of the game problem of soft landing for moving object. Cybernetics and Systems Analysis. 2001. Vol. 37, N 1. P. 75–91.

  23. Chikrii A.A. An analytical method in dynamic pursuit games. Proc. of the Steklov Institute of Mathematics. 2010. Vol. 271. P. 69–85.

  24. Chikrii A.A. Game dynamic problems for systems with fractional derivatives. Springer Optimization and Its Applications. 2008. Vol. 17. P. 349–387.

  25. Rockefellar R.. Convex analysis [Russian translation]. Moscow: Mir, 1973. 470 p.

  26. Filippov A.F. On some issues of the theory of optimal regulation. Vestn. Moscow State University. Ser. mathematics, mechanics, astronomy, physics, chemistry. 1959. No. 2. P. 25–32.

  27. Polovinkin E.S. Elements of the theory of multivalued mappings [in Russian]. Moscow: MIPT Publishing House, 1982. 127 p.

  28. Aubin J.-P., Frankowska H. Set-valued analysis. Boston; Basel; Berlin: Birkhauser, 1990. 461 p.

  29. Ioffe A.D., Tikhomirov V.M. Theory of extremal problems [in Russian]. Moscow: Nauka, 1974. 480 p.

Editorial Board Announcements Abstracts Authors Archive
about scope office editorial board instructions for authors subscriptions contacts
© 2019 Kibernetika.org. All rights reserved.