ON A DYNAMIC GAME PROBLEM WITH AN INDECOMPOSABLE SET OF DISTURBANCES

Dmitriy A. Serkov     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620990, Russian Federation)

Abstract


For an abstract dynamic system, a game problem of retention of the motions in a given set of the motion histories is considered. The case of an indecomposable set of disturbances is studied. The set of successful solvability and a construction of a resolving quasistrategy based on the method of programmed iterations is proposed.


Keywords


Indecomposable disturbances, Quasistrategy, Retention problem

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References


  1. Chentsov A.G. On a game problem of converging at a given instant of time. Math. USSR-Sb., 1976. Vol. 28, No. 3. P. 353–376. DOI: 10.1007/s40840-014-0068-y
  2. Chentsov A.G. On a game problem of guidance with information memory. Dokl. Akad. Nauk SSSR, 1976. Vol. 227, No. 2. P. 306–309. (in Russian) http://mi.mathnet.ru/eng/dan40223
  3. Engelking R. General Topology. Sigma Ser. Pure Math., vol. 6. Warszawa: Panstwowe Wydawnictwo Naukowe, 1985. 540 p.
  4. Gomoyunov M.I., Serkov D.: Control with a guide in the guarantee optimization problem under functional constraints on the disturbance. Proc. Steklov Inst. Math., 2017. Vol. 299, Suppl. 1. P. S49–S60. DOI: 10.1134/S0081543817090073
  5. Krasovskii N.N., Subbotin A.I. Game-Theoretical Control Problems. New York: Springer-Verlag, 1988. 517 p.
  6. Ledyaev Y.S. Program-predictive feedback control for systems with evolving dynamics. IFAC-PapersOnLine, 2018. Vol. 51, No. 32. P. 723–726. DOI: 10.1016/j.ifacol.2018.11.461
  7. Rockafellar R.T. Integrals which are convex functionals. Pacific J. Math., 1968. Vol. 24, No. 3. P. 525–539. DOI: 10.2140/pjm.1968.24.525
  8. Serkov D.A. Transfinite sequences in the programmed iteration method. Proc. Steklov Inst. Math., 2018. Vol. 300, Suppl. 1. P. S153–S164. DOI: 10.1134/S0081543818020153
  9. Serkov D.A., Chentsov A.G. The elements of the operator convexity in the construction of the programmed iteration method. Bull. South Ural State Univ. Ser. Math. Modell. Program. Comp. Software, 2016. Vol. 9, No. 3. P. 82–93. DOI: 10.14529/mmp160307



DOI: http://dx.doi.org/10.15826/umj.2019.2.007

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