Davydov, A.A. & Shutkina, T.S.
(2011).
*Uniqueness of a cycle with discounting that is optimal with respect to the average time profit.*
Proceedings of the Institute of Mathematics and Mechanics UrB RAS 17 (2) 80-87.

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Average optimization; Periodic process; Necessary optimality condition; Discounting |

Research Programs: | Advanced Systems Analysis (ASA) |

Bibliographic Reference: | Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences; 17(2):80-87 |

Depositing User: | IIASA Import |

Date Deposited: | 15 Jan 2016 08:45 |

Last Modified: | 27 Aug 2021 17:39 |

URI: | https://pure.iiasa.ac.at/9593 |

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