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Resolving-Functions Method for Game Problems of Control with Integral Constraints

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Cybernetics and Systems Analysis Aims and scope

Abstract

The method of resolving functions is investigated as applied to game problems of control with integral constraints. A scheme of the method is proposed that ensures the end of a game within a definite guaranteed time in the class of stroboscopic strategies. The results of comparison of the guaranteed times of this scheme of the resolving-functions method with those of the first direct Pontryagin method for integral constraints are shown.

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References

  1. M. S. Nikol’skii, “A direct method in linear differential games with integral constraints,” Controllable Systems, Iss. 2, 49–59 (1969).

  2. A. A. Chikrii and V. V. Bezmagorychnyi, “Method of resolving functions in linear differential games with integral constraints,” Avtomatika, No. 4, 26–36 (1993).

  3. A. A. Chikrii and A. A. Belousov, “On linear differential games with integral constraints,” Trudy Inst. Mat. i Mekh. UrO RAN, Vol. 15, No. 4, 290–301 (2009).

    Google Scholar 

  4. B. T. Samatov, “Problems of group pursuit with integral constraints on controls of the players. I,” Cybernetics and Systems Analysis, Vol. 49, No. 5, 756–767 (2013).

    Article  MathSciNet  Google Scholar 

  5. A. A. Chikrii, Conflict Controlled Processes, Springer Science and Business Media (2013).

  6. A. A. Chikrii and I. S. Rappoport, “Method of resolving functions in the theory of conflict-controlled processes,” Cybernetics and Systems Analysis, Vol. 48, No. 4, 512–531 (2012).

    Article  MathSciNet  Google Scholar 

  7. A. A. Chikriy and V. K. Chikrii, “Image structure of multivalued mappings in game problems of movement control,” Journal of Automation and Information Science, Vol. 48, No. 3, 20–35 (2016).

    Article  Google Scholar 

  8. I. S. Rappoport, “Sufficient conditions of the guaranteed result in differential game with a terminal payoff function,” Journal of Automation and Information Science, Vol. 50, No. 2, 14–27 (2018).

    Article  Google Scholar 

  9. O. Hajek, Pursuit Games, Vol. 12, Academic Press, New York (1975).

    MATH  Google Scholar 

  10. I. S. Rappoport, “Stroboscopic strategy in the method of resolving functions for game control problems with terminal payoff function,” Cybernetics and Systems Analysis, Vol. 52, No. 4, 577–587 (2016).

    Article  MathSciNet  Google Scholar 

  11. J. S. Rappoport, “Resolving-functions method in the theory of conflict-controlled processes with terminal payoff function,” Journal of Automation and Information Science, Vol. 48, No. 5, 74–84 (2016).

    Article  Google Scholar 

  12. N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).

    MATH  Google Scholar 

  13. L. S. Pontryagin, Selected Scientific Works [in Russian], Vol. 2, Nauka, Moscow (1988).

    Google Scholar 

  14. M. S. Nikolskii, L. S. Pontryagin’s First Direct Method in Differential Games [in Russian], MSU Publishing House, Moscow (1984).

    Google Scholar 

  15. M. V. Pittsyk and A. A. Chikrii, “On a group pursuit problem,” Journal of Applied Mathematics and Mechanics. Vol. 46, No. 5, 584–589 (1982).

    Article  MathSciNet  Google Scholar 

  16. Yu. V. Pilipenko and A. A. Chikrii, “Oscillatory conflict-control processes,” Journal of Applied Mathematics and Mechanics, Vol. 57, No. 3, 407–581 (1993).

    Article  MathSciNet  Google Scholar 

  17. A. A. Chikrii, “Multivalued mappings and their selections in game control problems,” Journal of Automation and Information Sciences, Vol. 27, No. 1, 27–38 (1995).

    MathSciNet  Google Scholar 

  18. A. A. Chikrii, “Quasilinear controlled processes under conflict,” Journal of Mathematical Sciences, Vol. 80, No. 3, 1489–1518 (1996).

    Article  MathSciNet  Google Scholar 

  19. A. A. Chikrii and S. D. Eidel’man, “Generalized Mittag-Leffler matrix functions in game problems for evolutionary equations of fractional order,” Cybernetics and Systems Analysis, Vol. 36, No. 3, 315–338 (2000).

    Article  MathSciNet  Google Scholar 

  20. A. A. Chikrii and S. D. Eidelman, “Control game problems for quasilinear systems with Riemann–Liouville fractional derivatives,” Cybernetics and Systems Analysis, Vol. 37, No. 6, 836–864 (2001).

    Article  MathSciNet  Google Scholar 

  21. A. A. Chikrii, “Optimization of game interaction of fractional-order controlled systems,” Optimization Methods and Software, Vol. 23, No. 1, 39–72 (2008).

    Article  MathSciNet  Google Scholar 

  22. A. A. Chikrii, “An analytical method in dynamic pursuit games,” in Proc. Steklov Institute of Mathematics, Vol. 271, 69–85 (2010).

    Article  MathSciNet  Google Scholar 

  23. A. A. Chikrii, “Game dynamic problems for systems with fractional derivatives.” Springer Optimization and Its Applications, Vol. 17, 349–387 (2008).

    Article  MathSciNet  Google Scholar 

  24. R. Rokafellar, Convex Analysis [Russian translation], Mir, Moscow (1973).

    Google Scholar 

  25. A. F. Filippov, “On some questions in the theory of optimal regulation,” Vestn. Moskov. Univ., Ser. Mathematics, Mechanics, Astronomy, Physics, and Chemistry, No. 2, 25–32 (1959).

  26. E. S. Polovinkin, Elements of the Theory of Multivalued Mappings [in Russian], MFTI, Moscow (1982).

    Google Scholar 

  27. J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston–Basel–Berlin (1990).

  28. A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

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Authors and Affiliations

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

    J. S. Rappoport

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  1. J. S. Rappoport
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Correspondence to J. S. Rappoport.

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2018, pp. 109–127.

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Rappoport, J.S. Resolving-Functions Method for Game Problems of Control with Integral Constraints. Cybern Syst Anal 54, 779–795 (2018). https://doi.org/10.1007/s10559-018-0080-6

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  • DOI: https://doi.org/10.1007/s10559-018-0080-6

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