A. A. Davydov, H. Mena-Matos, C. S. Moreira, “Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems”, CMFD, 2011, Volume 42,Pages <nobr>95

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

A. A. Davydov^ab, H. Mena-Matos^c, C. S. Moreira^c

^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.

UDC: 517.938