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Journal of Automation and Information Sciences

Published 12 issues per year

ISSN Print: 1064-2315

ISSN Online: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

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Sufficient Conditions for the Approach of Controlled Objects with Various Inertia in Game Dynamics Problems

Volume 52, Issue 11, 2020, pp. 28-47
DOI: 10.1615/JAutomatInfScien.v52.i11.30
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ABSTRACT

The paper considers the approach problem of controlled objects with different inertia in game dynamics problems based on modern version of the resolving functions method. For controlled objects with different inertia it is characteristic that on a certain time interval the Pontrygin condition is not fulfilled that significantly complicates the application of the resolving functions method to this class of game dynamics problems. Consideration is given to the case when the general scheme of the resolving functions method is based on the analog of the modified Pontryagin condition taking into account the terminal set. For solving such problems the paper proposes the method associated with constructing some scalar functions which qualitatively characterize the course of controlled objects approach and the efficiency of the decisions made. Such functions are called resolving. The attractiveness of the resolving functions method lies in the fact that it enables one to use effectively the modern technique of multivalued mappings to substantiate game construction and to obtain meaningful results on their basis. In any forms of the resolving functions method the main principle is the accumulative one used in the current summation of the resolving function to estimate the quality of the first player game until a certain threshold is reached. The guaranteed game termination times for the considered schemes of controlled objects approach with different inertia are compared. The example is given.

REFERENCES
  1. Chikrii A.A., Conflict controlled processes, Springer Science and Business Media, 2013.

  2. Chikrii A.A., An analytical method in dynamic pursuit games, Proceedings of the Steklov Institute of Mathematics, 2010, 271, 69-85.

  3. Chikrii A. A., Chikrii V.K., Image structure of multivalued mappings in game problems of motion control, Journal of Automation and Information Sciences, 2016, 48, No. 3, 20-35.

  4. Chikrii A.A., Upper and lower resolving functions in game problems of dynamics, Trudy IMM UrO RAN, 2017, 23, No. 1, 293-305.

  5. Krasovskiy N.N., Subbotin A.I., Positional differential games [in Russian], Nauka, Moscow, 1974.

  6. Pontryagin L.S., Selected research papers [in Russian], Nauka, Moscow, 1988.

  7. Subbotin A.I., Chentsov A.G., Guarantee optimization in control problems [in Russian], Nauka, Moscow, 1981.

  8. Hajek O., Pursuit games, Academic Press, New York, 1975, 12.

  9. Aubin J.-P., Frankowska H., Set-valued analysis, Birkhauser, Boston; Basel; Berlin, 1990.

  10. Rockafellar R., Convex analysis [Russian translation], Mir, Moscow, 1973.

  11. Ioffe A.D., Tikhomirov V.M., Extreme problem theory [in Russian], Nauka, Moscow, 1974.

  12. Chikrii A.A., Rappoport I.S., Resolving functions method in the theory of conflict-controlled processes, Kibernetika i sistemnyi analiz, 2012, 48, No. 4, 40-64.

  13. Chikrii A.A., Multivalued mappings and their selections in game control problems, Journal of Automation and Information Sciences, 1995, 27, No. 1, 27-38.

  14. Pittsyk M.V., Chikrii A.A., On group pursuit problem, Journal of Applied Mathematics and Mechanics, 1982, 46, No. 5, 584-589.

  15. Chikrii A.A., Dzyubenko K.G., Bilinear Markov processes of searching for moving objects, Problemy upravleniya i informatiki, 1997, No. 1, 92-107.

  16. Eidelman S.D., Chikrii A.A., Dynamic game problems of approach for fractional-order equations, Ukrainian Mathematical Journal, 2000, 52, No. 11, 1787-1806.

  17. Chikrii A.A., Game dynamic problems for systems with fractional derivatives, Springer Optimization and its Applications, 2008, 17, 349-387.

  18. Pilipenko Yu.V., Chikrii A.A., Oscillatory conflict-controlled processes, Prikladnaya matematika i mekhanika, 1993, 57, No. 3, 3-14.

  19. Chikrii A.A., Quasilinear controlled processes under conflict, Journal of Mathematical sciences, 1996, 80, No. 3, 1489-1518.

  20. Chikrii A.A., Eidelman S.D., Game control problems for quasi-linear systems with fractional Rimmann-Liouville derivatives, Kibernetika i sistemnyi analiz, 2001, No. 6, 66-99.

  21. Chikrii A.A., Optimization of game interaction of fractional-order controlled systems, Optimization Methods and Software, 2008, 23, No. 1, 39-72.

  22. Chikrii A. A., Eidelman S.D., Generalized matrix Mittag-Leffler functions in game problems for evolutionary equations of fractional order, Kibernetika i sistemnyi analiz, 2000, No. 3, 3-32.

  23. Filippov A.F., On some matters of optimal control theory, Vestnik MGU. Ser. Matematika, mekhanika, astronomiya, fizika, khimiya, 1959, No. 2, 25-32.

  24. Polovinkin E.S., Elements of multivalued mappings theory [in Russian], Izdatelstvo MFTI, Moscow, 1982.

  25. Rappoport I.S., On Guaranteed result in game problems of controlled objects approach, Journal of Automation and Information Sciences, 2020, 52, No. 3, 48-64, DOI: 10.1615/JAutomatInfScien. v52.i3.40.

  26. Belousov A.A., Kuleshyn V.V., Vyshenskiy V.I., Real-time algorithm for calculation of the distance of the interrupted take-off, Journal of Automation and Information Sciences, 2020, 52, No. 4, 38-46, DOI: 10.1615/JAutomatInfScien.v52.i4.40.

  27. Chikriy A.A., Chikrii G.T., Volyanskiy K.Yu., Quasilinear positional integral games of approach, Journal of Automation and Information Sciences, 2001, 33, No. 10, 31-43, DOI: 10.1615/ JAutomatInfScien.v3 3.i10.40.

  28. Chikrii G.T., Principle of time stretching in evolutionary games of approach, Journal of Automation and Information Sciences, 2016, 48, No. 5, 12-26, DOI: 10.1615/ JAutomatInfScien.v48.i5.20.

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