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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 517.977
I.S. Rappoport1


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

jeffrappoport@gmail.com

SUFFICIENT CONDITIONS OF APPROACH OF THE CONTROLLED OBJECTS
IN DYNAMIC GAME PROBLEMS. II

Abstract. The problem of approach of control objects is solved on the basis of the method of resolving functions. New sufficient conditions for game termination in a finite guaranteed time are proposed for the case where the Pontryagin condition is not satisfied. Resolving functions of special type are introduced and are used to develop two schemes of the method of resolving functions that ensure termination of the differential game in the class of quasi-strategies and counter-controls. The formulas for calculating the resolving functions are given. The results are illustrated by a model example.

Keywords: quasilinear differential game, multivalued mapping, measurable selector, stroboscopic strategy, resolving function.



FULL TEXT

REFERENCES

  1. Chikriy A.A., Rappoport I.S. The method of resolving functions in the theory of conflict-controlled processes. Kibernetika i sistemnyj analiz. 2012. Vol. 48, N 5. P. 40–64.

  2. Chikrii A.A. Upper and lower resolving functions in game dynamics problems. Tr. IMM UB RAS. 2017. Vol. 23, N 1. P. 293–305.

  3. Krasovsky N.N., Subbotin A.I. Positional differential games. Moscow: Nauka, 1974. 455 p.

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

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

  6. Subbotin A.I., Chentsov A.G. Optimization of guarantee in control problems. Moscow: Nauka, 1981. 288 p.

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

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

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

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

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

  12. 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.

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

  14. Chikrii A.A., Dzyubenko K.G. Bilinear Markov processes of searching for moving targets. Journal of Automation and Information Sciences. 2001. Vol. 33, N 5–8. P. 62–74.

  15. Chikrii A.A., Eidelman S.D. Game problems for fractional quasilinear systems. Journal Computers and Mathematics with Applications. 2002. Vol. 44. P. 835–851.

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

  17. Pilipenko Yu.V., Chikrii A.A. Oscillating conflict-driven processes. Prikl. matematika i mekhanika. 1993. Vol. 57, N 3. P. 3–14.

  18. Chikrii A.A. Quasilinear controlled processes under conflict. Journal of Mathematical Sciences. 1996. Vol. 80, N 3. P. 1489–1518.

  19. Chikriy A.A., Eidelman S.D. Game control problems for quasilinear systems with fractional Riemann – Liouville derivatives. Kibernetika i sistemnyj analiz. 2001. N 6. P. 66–99.

  20. Chikrii A.A. Optimization of game interaction of fractional-order controlled systems. Optimization Methods and Software. 2008. Vol. 23, N 1. P. 39–72.

  21. Rappoport I.S. On the stroboscopic strategy in the method of resolving functions for game control problems with the terminal pay function. Kibernetika i sistemnyj analiz. 2016. Vol. 52, N 4. P. 90–102.

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

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

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