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On the stability of a procedure for solving a minimax control problem for a positional functional

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Abstract

We consider a minimax feedback control problem for a linear dynamic system with a positional quality criterion, which is the norm of the family of deviations of the motion from given target points at given times. The problem is formalized as a positional differential game. A procedure for calculating the value of the game based on the backward construction of upper convex hulls of auxiliary program functions is studied. We also study a method of generating a minimax control law based on this procedure and on the extremal shift principle. The stability of the proposed resolving constructions with respect to computational and informational noises is proved.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    M. I. Gomoyunov & N. Yu. Lukoyanov

  2. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620000, Russia

    N. Yu. Lukoyanov

Authors
  1. M. I. Gomoyunov
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  2. N. Yu. Lukoyanov
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Correspondence to M. I. Gomoyunov.

Additional information

Original Russian Text © M.I.Gomoyunov, N.Yu. Lukoyanov, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 1.

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Gomoyunov, M.I., Lukoyanov, N.Y. On the stability of a procedure for solving a minimax control problem for a positional functional. Proc. Steklov Inst. Math. 288 (Suppl 1), 54–69 (2015). https://doi.org/10.1134/S0081543815020078

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  • DOI: https://doi.org/10.1134/S0081543815020078

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