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 CMFD, 2011, Volume 42, Pages 95–117 (Mi cmfd193)

Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems

A. A. Davydovab, H. Mena-Matosc, C. S. Moreirac

a Vladimir State University, Russia
b IIASA, Austria
c Universidade do Porto and Centro de Matemática da Universidade do Porto, Portugal

Abstract: 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 $k\le2$ and the maximum is provided by level cycles.

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English version:
Journal of Mathematical Sciences, 2014, 199:5, 510–534

Bibliographic databases:

Document Type: Article
UDC: 517.938

Citation: A. A. Davydov, H. Mena-Matos, C. S. Moreira, “Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems”, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), CMFD, 42, PFUR, M., 2011, 95–117; Journal of Mathematical Sciences, 199:5 (2014), 510–534

Citation in format AMSBIB
\Bibitem{DavMenMor11} \by A.~A.~Davydov, H.~Mena-Matos, C.~S.~Moreira \paper Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems \inbook Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3--7, 2009) \serial CMFD \yr 2011 \vol 42 \pages 95--117 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd193} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013831} \transl \jour Journal of Mathematical Sciences \yr 2014 \vol 199 \issue 5 \pages 510--534 \crossref{https://doi.org/10.1007/s10958-014-1879-y} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902782655} 

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This publication is cited in the following articles:
1. Davydov A.A., Mena-Matos H., Moreira C.S., “Generic Profit Singularities in Time Averaged Optimization For Phase Transitions in Polydynamical Systems”, J. Math. Anal. Appl., 424:1 (2015), 704–726
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