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 Arnold’s theorem on the uniqueness of such a cycle in the case when the profit gathered along the cycle is not discounted.
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Original Russian Text © A.A. Davydov, T.S. Shutkina, 2011, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Vol. 17, No. 2.
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Davydov, A.A., Shutkina, T.S. Uniqueness of a cycle with discounting that is optimal with respect to the average time profit. Proc. Steklov Inst. Math. 276 (Suppl 1), 80–87 (2012). https://doi.org/10.1134/S008154381202006X
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DOI: https://doi.org/10.1134/S008154381202006X