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On the Relation between the Properties of a Degenerate Linear-Quadratic Control Problem and the Euler–Poisson Equation

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Abstract

A quadratic functional with linear constraints in the form of differential equations with identically degenerate matrices multiplying the derivative of the state vector function is considered. The structure of the general solutions of such systems and some of their properties are discussed. On this basis, the conditions for the non-negativity of the objective functional and small deviation of the control from the stationary point for small values of the functional are obtained.

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Funding

This work was supported in part by the Russian Foundation for Basic Research (project no. 18-01-00643).

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, 664033, Irkutsk, Russia

    V. F. Chistyakov & E. V. Chistyakova

  2. Institute of Mathematics, Vietnam Academy of Science and Technologies, Hanoi, Vietnam

    Ta Zui Fuong

Authors
  1. V. F. Chistyakov
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  2. E. V. Chistyakova
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  3. Ta Zui Fuong
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Corresponding authors

Correspondence to V. F. Chistyakov, E. V. Chistyakova or Ta Zui Fuong.

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Translated by E. Chernokozhin

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Chistyakov, V.F., Chistyakova, E.V. & Fuong, T.Z. On the Relation between the Properties of a Degenerate Linear-Quadratic Control Problem and the Euler–Poisson Equation. Comput. Math. and Math. Phys. 60, 390–403 (2020). https://doi.org/10.1134/S0965542520030069

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  • DOI: https://doi.org/10.1134/S0965542520030069

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