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On players interaction in hierarchical system under uncertain conditions: Solution based on penalty functions approach

  • Control Systems and Information Technologies
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Abstract

Optimal interaction scheme in two-level hierarchical system is suggested. Convergence of the penalty function method having the proposed form is demonstrated. The problem of transition from iterative limits with respect to penalty parameters to standard limits is solved through their coordination.

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References

  1. Savage, L.Y., The Theory of Statistical Decision, J. Am. Stat. Assoc., 1951, no. 46, pp. 55–67.

  2. Germeier, Yu.B., Igry s neprotivopolozhnymi interesami (Games with Non-antagonistic Interests), Moscow: Nauka, 1976.

    Google Scholar 

  3. Germeier, Yu.B., An Approximate Reduction via Penalty Functions of a Problem of Determining a Maximin to a Problem of Determining a Maximum, Zh. Vychisl. Mat. Mat. Fiz., 1969, vol. 9, no. 3, pp. 730–731.

    MathSciNet  Google Scholar 

  4. Fedorov, V.V., Chislennye metody maksimina (Numerical Maximin Methods), Moscow: Nauka, 1979.

    Google Scholar 

  5. Gorelik, V.A., Maximin Problems on Dependent Sets in Banach Spaces, Kibernetika, 1983, no. 1, pp. 64–67.

  6. Gorelik, V.A. and Tarakanov, A.F., Penalty Method for Nonsmooth Minimax Control Problems with Interdependent Variables, Kibernetika, 1989, no. 4, pp. 52–56.

  7. Gorelik, V.A., Gorelov, M.A., and Kononenko, A.F., Analiz konfliktnykh situatsii v sistemakh upravleniya (Analysis of Conflict Situations in Control Systems), Moscow: Radio i Svyaz’, 1991.

    Google Scholar 

  8. Govorov, A.N. and Tarakanov, A.F., Penalty Method and Necessary Optimality Conditions in a Statistical Hierarchic Game with Uncertainty, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2005, no. 2, pp. 46–51.

  9. Fedorov, V.V., Conditions for Regularity and Necessary Conditions for a Maximin with Dependent Variables, Zh. Vychisl. Mat. Mat. Fiz., 1977, vol. 17, no. 1, pp. 79–90.

    MATH  Google Scholar 

  10. Germeier, Yu.B., On the Problem of Finding a Maximum with Constraints, Zh. Vychisl. Mat. Mat. Fiz., 1970, vol. 10, no. 1, pp. 39–54.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Computing Centre, Russian Academy of Sciences, Moscow, Russia

    V. A. Gorelik

  2. State Teachers’ Training Institute, Borisoglebsk, Russia

    A. V. Rodyukov & A. F. Tarakanov

Authors
  1. V. A. Gorelik
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  2. A. V. Rodyukov
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  3. A. F. Tarakanov
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Additional information

Original Russian Text © V.A. Gorelik, A.V. Rodyukov, A.F. Tarakanov, 2008, published in Sistemy Upravleniya i Informatsionnye Tekhnologii, 2008, No. 4, pp. 52–56.

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Gorelik, V.A., Rodyukov, A.V. & Tarakanov, A.F. On players interaction in hierarchical system under uncertain conditions: Solution based on penalty functions approach. Autom Remote Control 73, 198–205 (2012). https://doi.org/10.1134/S0005117912010195

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  • DOI: https://doi.org/10.1134/S0005117912010195

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