Geodesic
Uniqueness of a cycle with discounting that is optimal with respect to the average time profit
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 80-87

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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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     title = {Uniqueness of a cycle with discounting that is optimal with respect to the average time profit},
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A. A. Davydov; T. S. Shutkina. Uniqueness of a cycle with discounting that is optimal with respect to the average time profit. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 80-87. http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a7/