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The variational stability of an optimal control problem for Volterra-type equations

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Abstract

We study the variational stability of an optimal control problem for a Volterra-type nonlinear functional-operator equation. This means that for this optimal control problem (P ɛ ) with a parameter ɛ we study how its minimum value min(P ɛ ) and its set of minimizers argmin(P ɛ ) depend on ɛ. We illustrate the use of the variational stability theorem with a series of particular problems.

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Authors and Affiliations

  1. Institute for System Dynamics and Control Theory, Irkutsk, Russia

    N. I. Pogodaev & A. A. Tolstonogov

Authors
  1. N. I. Pogodaev
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  2. A. A. Tolstonogov
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Correspondence to N. I. Pogodaev.

Additional information

Original Russian Text Copyright © 2014 Pogodaev N.I. and Tolstonogov A.A.

The authors were supported by the Russian Foundation for Basic Research (Grant 13-01-00287-a) and the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (Contract No. 8211 of 06.08.2012).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 4, pp. 818–839, July–August, 2014.

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Pogodaev, N.I., Tolstonogov, A.A. The variational stability of an optimal control problem for Volterra-type equations. Sib Math J 55, 667–686 (2014). https://doi.org/10.1134/S0037446614040090

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  • DOI: https://doi.org/10.1134/S0037446614040090

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