Automation and Remote Control

, Volume 79, Issue 10, pp 1929–1952 | Cite as

Mathematical Foundations of the Golden Rule. II. Dynamic Case

  • V. I. ZhukovskiyEmail author
  • L. V. Smirnova
  • A. S. Gorbatov
Mathematical Game Theory and Applications


This paper extends the earlier research of the Golden Rule in the static case [2] to the dynamic one. The main idea is to use the Germeier convolution of the payoff functions of players within the framework of antagonistic positional differential games in quasi motions and guiding control.


non-cooperative games positional strategy saddle point Berge equilibrium 


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  1. 1.
    Germeier, Yu.B., Vvedenie v teoriyu issledovaniya operatsii (Introduction to the Theory of Operations Research), Moscow: Nauka, 1971.Google Scholar
  2. 2.
    Zhukovskiy, V.I. and Kudryavtsev, K.N., Mathematical Foundations of the Golden Rule. I. Static Case, Autom. Remote Control, 2017, vol. 78, no. 10, pp. 1920–1940.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Zhukovskiy, V.I. and Salukvadze, M.E., Optimizatsiya garantii v mnogokriterial’nykh zadachakh upravleniya (Optimization of Guarantees in Multicriteria Control Problems), Tbilisi: Metsniereba, 1996.Google Scholar
  4. 4.
    Zhukovskiy, V.I. and Salukvadze, M.E., Nekotorye igrovye zadachi upravleniya i ikh prilozheniya (Some Games of Control and Their Applications), Tbilisi: Metsniereba, 1998.Google Scholar
  5. 5.
    Kononenko, A.F., Structure of Optimal Strategy in Dynamic Controlled Systems, Zh. Vychisl. Mat. Mat. Fiz., 1980, no. 5, pp. 1105–1116.zbMATHGoogle Scholar
  6. 6.
    Krasovskii, N.N., Upravlenie dinamicheskoi sistemoi (Control of a Dynamic System), Moscow: Nauka, 1985.Google Scholar
  7. 7.
    Krasovskii, N.N. and Subbotin, A.I., Pozitsionnye differentsial’nye igry (Positional Differential Games), Moscow: Nauka, 1985.zbMATHGoogle Scholar
  8. 8.
    Morozov, V.V., Sukharev, A.G., and Fedorov, V.V., Issledovanie operatsii v zadachakh i uprazhneniyakh (Operations Research in Problems and Exercises), Moscow: Vysshaya Shkola, 1986.Google Scholar
  9. 9.
    Subbotin, A.I. and Chentsov, A.G., Optimizatsiya garantii v zadachakh upravleniya (Optimization of Guarantee in Control Problems), Moscow: Nauka, 1981.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. I. Zhukovskiy
    • 1
    Email author
  • L. V. Smirnova
    • 2
  • A. S. Gorbatov
    • 1
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Razumovsky State University of Technologies and Management (the First Cossack University)MoscowRussia

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