Uniqueness of a Cycle with Discounting That Is Optimal with Respect to the Average Time Profit

作者：Davydov A A^*; Shutkina T S

来源：Proceedings of the Steklov Institute of Mathematics, 2012, 276: S80-S87.

DOI：10.1134/S008154381202006X

• average optimization
• periodic process
• necessary optimality condition
• discount

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.

• 出版日期2012-4