Author: Arnold V.I.
Publisher: Springer Publishing Company
ISSN: 0016-2663
Source: Functional Analysis and Its Applications, Vol.36, Iss.2, 2002-04, pp. : 83-92
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Abstract
The time mean of a smooth objective function along a phase trajectory of a controlled dynamical system is maximized. The simplest singularities of the dependence of the optimal mean value on the parameter in generic one-parameter families of controlled systems of this kind are listed. It turns out that the most common generic stable singularity is the discontinuity of the first or second derivative of the optimal mean value with respect to the parameter.
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