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Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 2, Pages 80–87 (Mi timm698)  

Uniqueness of a cycle with discounting that is optimal with respect to the average time profit

A. A. Davydov, T. S. Shutkina

Vladimir State University

Abstract: For cyclic processes modeled by periodic motions of a continuous control system on a circle, we prove the uniqueness of a cycle maximizing the average one-period time profit in the case of discounting provided that the minimum and maximum velocities of the system coincide at some points only and the profit density is a differentiable function with a finite number of critical points. The uniqueness theorem is an analog of Arnolds theorem on the uniqueness of such a cycle in the case when the profit gathered along the cycle is not discounted.

Keywords: average optimization, periodic process, necessary optimality condition, discounting.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, 276, suppl. 1, S80–S87

Bibliographic databases:

UDC: 517.977.1
Received: 10.10.2010

Citation: A. A. Davydov, T. S. Shutkina, “Uniqueness of a cycle with discounting that is optimal with respect to the average time profit”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 2, 2011, 80–87; Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S80–S87

Citation in format AMSBIB
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\paper Uniqueness of a cycle with discounting that is optimal with respect to the average time profit
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 2
\pages 80--87
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2012
\vol 276
\issue , suppl. 1
\pages S80--S87
\crossref{https://doi.org/10.1134/S008154381202006X}
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