Suscripción a Biblioteca: Guest
Journal of Automation and Information Sciences

Publicado 12 números por año

ISSN Imprimir: 1064-2315

ISSN En Línea: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

Indexed in

Method of Resolving Functions in the Group Pursuit Problem with a Terminal Pay Off Function and Integral Constraints on Controls

Volumen 51, Edición 4, 2019, pp. 24-42
DOI: 10.1615/JAutomatInfScien.v51.i4.30
Get accessGet access

SINOPSIS

A method is proposed for solving game dynamics problems with a terminal pay off function and integral constraints on controls which consists in systematical using the ideas of Fenhel−Moreau as applied to the general scheme of resolving functions method. The essence of the proposed method lies in the fact that the resolving function can be expressed in terms of the function conjugate to the pay off function and using the involute of the conjugation operator for a convex closed function to obtain a guaranteed estimate of the terminal value of the pay off function which is represented by the paying off value at the initial time instant and the integral of the resolving function. The main feature of the method is the cumulative principle used in the current summation of the resolving function for estimating the game quality until a certain threshold value is reached. The paper considers linear differential games of group pursuit with a terminal pay off function and integral constraints on controls. Sufficient conditions for the game completion in a finite guaranteed time in a class of quasi-strategies are formulated. Two schemes of the resolving functions method are proposed that ensure without additional assumptions the game completion in the final guaranteed time in the class of stroboscopic strategies. The results of comparing the guaranteed times of different schemes of the resolving functions method are presented.

REFERENCIAS
  1. Rappoport I.S., Chikrii A.A., On a guaranteed result in a differential game with terminal pay off function, Prikladnaya matematika i mekhanika, 1995, 59, No. 5, 714-720.

  2. Rappoport I.S., Chikrii A.A., Guaranteed result in differential group pursuit game with terminal pay off function, Prikladnaya matematika i mekhanika, 1997, 61, No. 4, 584-594.

  3. Rappoport I.S., Resolving function method in theory of conflict-controlled processes with terminal pay off function, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal ''Problemy upravleniya i informatiki'' , 2016, No. 3, 49-58.

  4. Rappoport I.S., On stroboscopic strategy in resolving functions method for game control problems with terminal pay off function, Kibernetika i sistemnyi analiz, 2016, 52, No. 4, 90-102.

  5. Rappoport I.S., Sufficient conditions of guaranteed result in differential game with terminal pay off function, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal ''Problemy upravleniys i informatiki'', 2018, No. 1, 72-84.

  6. Nikolskiy M.S., Direct method in linear differential games with integral constraint, Upravlyaemyye sistemy, 1969, No. 2, 49-59.

  7. Chikrii A.A., Bezmagorychnyi V.V., Resolving functions method in linear differential games with integral constraints, Avtomatika, 1993, No. 4, 26-36.

  8. Chikrii A.A., Belousov A.A., On linear differential games with integral constraints of approach, Trudy IMM UrO RAN, 2009, 15, No. 4, 290-301.

  9. Samatov B.T., On group pursuit problems under integral constraints on controls. I, Kibernetika i sistemnyi analiz, 2013, 49, No. 5, 132-145.

  10. Rappoport I.S., Resolving functions method for game control problems with integral constraint, Kibernetika i sistemnyi analiz, 2018, 54, No. 5, 109-127.

  11. Chikrii A.A., Conflict controlled processes, Springer Science and Business Media, Dordrecht, Boston; London, 2013.

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

  13. Hajek O., Pursuit Games, Academic Press, New York, 1975, 12.

  14. Pshenichnyi B.N., Simple pursuit by some objects, Kibernetika, 1976, No. 3, 145-146.

  15. Pshenichnyi B.N., Rappoport I.S., On one group pursuit problem, Kibernetika, 1979, No. 6, 145-146.

  16. Pshenichnyi B.N., Chikrii A.A., Rappoport I.S., Efficient method for solving differential games with many pursuers, Doklady AN SSSR, 1981, 256, No. 3, 530-535.

  17. Pshenichnyi B.N., Chikrii A.A., Rappoport I.S., Pursuit by some controlled objects under phase constraints, Doklady AN SSSR, 1981, 259, No. 4, 785-788.

  18. Pshenichnyi B.N., Chikrii A.A., Rappoport I.S., Group pursuit in differential games, Techische Hochschul Leipzig, Wissenshaftliche Zeitschriff, 1982, No. 1, 13-27.

  19. Rappoport I.S., Group approach strategies in resolving functions method for quasi-linear conflict-controlled processes, Kibernetika i sistemnyi analiz, 2019, 55, No. 1, 149-163.

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

  21. Chikrii A.A., Eidelman S.D., Game problems for fractional quasilinear systems, Int. J. Computers and Mathematics with Applications, 2002, 44, No. 7, 835-852.

  22. Chikrii A.A., Chikrii G.T., Matrix resolving functions in game problems of dynamics, Proceedings of the Steklov Institute of Mathematics, 2015, 291, 56-65.

  23. Nikolskiy M.S., L.S. Pontryagin first direct method in differential games [in Russian], Izdatelstvo MGU, Moscow, 1984.

  24. Grigorenko N.L., Mathematical control methods of some dynamic processes [in Russian], Izdatelstvo MGU, Moscow, 1990.

  25. Pshenichnyi B.N., Ostapenko V.V., Differential games [in Russian], Naukova dumka, Kiev, 1992.

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

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

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

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

  30. Chikrii A.A., Kalashnikova S.F., Pursuit of a group of evaders by a single controlled object, Cybernetics, 1987, 23, No. 4, 437-445.

  31. Chikrii A.A., Eidelman S.D., Generalized Mittag-Leffler matrix functions in game problems for evolutionary equations of fractional order, Kibernetika i sistemnyi analiz, 2000, 36, No. 3, 3-32.

  32. 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 Analisis, 2001, 37, No. 1, 75-91.

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

  34. Fillipov A.F., On some matters of optimal control theory, VestnikMGU, Ser. matematika, mekhanika, astronomiya, fizika, khimiya, 1959, No. 2, 25-32.

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

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

Portal Digitalde Biblioteca Digital eLibros Revistas Referencias y Libros de Ponencias Colecciones Precios y Políticas de Suscripcione Begell House Contáctenos Language English 中文 Русский Português German French Spain