Journal of Mathematical Sciences

, Volume 199, Issue 5, pp 510–534 | Cite as

Generic Profit Singularities in Time-Averaged Optimization for Cyclic Processes in Polydynamical Systems

  • A. A. Davydov
  • H. Mena-Matos
  • C. S. Moreira


We consider the optimization problem of maximizing the time-averaged profit for the motion of a smooth polydynamical system on the circle in the presence of a smooth profit density. If the problem depends on a k-dimensional parameter, then the optimal averaged profit is a function of the parameter. It is known from [4] that an optimal motion can always be selected among stationary strategies and a special type of periodic motions called level cycles. We present a classification of all generic singularities of the optimal averaged profit if k ≤ 2 and the maximum is provided by level cycles.


Smooth Function Normal Form Double Point Stationary Strategy Control Space 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Vladimir State UniversityRussia; IIASAAustria
  2. 2.Faculdade de Ciencias-Universidade do Porto and Centro de Matematica da Universidade do PortoPortoPortugal
  3. 3.University of Porto and CMUPPortoPortugal

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