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Differential Games on Minmax of the Positional Quality Index

Author

Listed:
  • Nikolai Lukoyanov

    (Ural Branch of the Russian Academy of Sciences
    Ural Federal University)

  • Mikhail Gomoyunov

    (Ural Branch of the Russian Academy of Sciences
    Ural Federal University)

Abstract

The paper goes back to the research of N. N. Krasovskii devoted to two-person zero-sum positional differential games on minmax of non-terminal quality indices, which evaluate a set of system’s states realized at given times. The first part of the paper gives a survey of the results concerning existence of the value and saddle point in such differential games. A special attention is paid to the case when the quality index has a certain positional structure. The second part of the paper overviews a method for constructing the value and optimal strategies in the case when the dynamical system is linear in the state vector, and the quality index has the appropriate convexity properties. The method is based on the recurrent procedure of constructing the upper convex hulls of certain auxiliary functions. To illustrate that this method can be numerically realized on modern computers, a model example is considered.

Suggested Citation

  • Nikolai Lukoyanov & Mikhail Gomoyunov, 2019. "Differential Games on Minmax of the Positional Quality Index," Dynamic Games and Applications, Springer, vol. 9(3), pages 780-799, September.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:3:d:10.1007_s13235-018-0281-7
    DOI: 10.1007/s13235-018-0281-7
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    References listed on IDEAS

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    1. Mikhail Gomoyunov & Dmitri Kornev & Nikolai Lukoyanov, 2014. "Game Theory Applications To Guarantee Optimization In Dynamical Systems With Control Delays," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-19.
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    Cited by:

    1. Mikhail Gomoyunov & Dmitriy Serkov, 2019. "On a Solution of a Guarantee Optimization Problem Under the Functional Constraints on the Disturbance," Dynamic Games and Applications, Springer, vol. 9(3), pages 700-723, September.

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