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

  • A. A. Davydov
  • T. S. Shutkina


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 Arnold’s theorem on the uniqueness of such a cycle in the case when the profit gathered along the cycle is not discounted.


average optimization periodic process necessary optimality condition discount 


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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Vladimir State UniversityVladimirRussia

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