Uniqueness of a cycle with discounting that is optimal with respect to the average time profit
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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 Arnold’s theorem on the uniqueness of such a cycle in the case when the profit gathered along the cycle is not discounted.
Keywordsaverage optimization periodic process necessary optimality condition discount
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