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Game Theory Applications To Guarantee Optimization In Dynamical Systems With Control Delays

Author

Listed:
  • MIKHAIL GOMOYUNOV

    (Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, S. Kovalevskaya str. 16, Ekaterinburg, 620990, Russia;
    Institute of Mathematics and Computer Sciences, Ural Federal University, Mira str. 19, Ekaterinburg, 620002, Russia)

  • DMITRI KORNEV

    (Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, S. Kovalevskaya str. 16, Ekaterinburg, 620990, Russia;
    Institute of Mathematics and Computer Sciences, Ural Federal University, Mira str. 19, Ekaterinburg, 620002, Russia)

  • NIKOLAI LUKOYANOV

    (Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, S. Kovalevskaya str. 16, Ekaterinburg, 620990, Russia;
    Institute of Mathematics and Computer Sciences, Ural Federal University, Mira str. 19, Ekaterinburg, 620002, Russia)

Abstract

In this paper, a linear dynamical system controlled under the conditions of disturbances and with control delays is considered. The Euclidean norm of a set of the system motion deviations at given instants of time from given targets is minimized. Within the game-theoretical approach the problem of calculating the value of the optimal guaranteed result and constructing a positional (closed-loop) control law that ensures this result is posed. For this problem, a solution procedure based on the recurrent construction of upper convex hulls of auxiliary program functions is elaborated. Results of numerical simulations are given.

Suggested Citation

  • 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.
  • Handle: RePEc:wsi:igtrxx:v:16:y:2014:i:02:n:s0219198914400106
    DOI: 10.1142/S0219198914400106
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    Citations

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    Cited by:

    1. 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.

    More about this item

    Keywords

    Feedback control; differential games; control delays; dynamic programming; 49N35; 49N70; 49L20;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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