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On some properties of the control problem under a program disturbance in a formalization based on the minimax risk (regret) criterion

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Abstract

A control problem under uncertainty for a system described by an ordinary differential equation with a terminal performance index is considered. The control and disturbance are subject to geometric constraints. The problem is formalized in classes of nonanticipating control strategies and program disturbances with the use of constructive ideal motions and the Savage minimax risk (regret) criterion. The properties of the used motion bundles are described and a number of relations characterizing the optimal risk function, which is an element of the formalization, are presented.

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Authors and Affiliations

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

    D. A. Serkov

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  1. D. A. Serkov
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Correspondence to D. A. Serkov.

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Original Russian Text © D.A. Serkov, 2010, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Vol. 16, No. 1.

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Serkov, D.A. On some properties of the control problem under a program disturbance in a formalization based on the minimax risk (regret) criterion. Proc. Steklov Inst. Math. 272 (Suppl 1), 152–164 (2011). https://doi.org/10.1134/S008154381102012X

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  • DOI: https://doi.org/10.1134/S008154381102012X

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