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Funktsional. Anal. i Prilozhen., 2002, Volume 36, Issue 2, Pages 1–11 (Mi faa186)  

This article is cited in 19 scientific papers (total in 20 papers)

Optimization in Mean and Phase Transitions in Controlled Dynamical Systems

V. I. Arnol'dab

a Université Paris-Dauphine
b Steklov Mathematical Institute, Russian Academy of Sciences

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.

Keywords: time mean, generic singularities, variational problems, mixed strategies, Harnack theorem, Sturm theorem


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English version:
Functional Analysis and Its Applications, 2002, 36:2, 83–92

Bibliographic databases:

UDC: 517.938
Received: 14.11.2001

Citation: V. I. Arnol'd, “Optimization in Mean and Phase Transitions in Controlled Dynamical Systems”, Funktsional. Anal. i Prilozhen., 36:2 (2002), 1–11; Funct. Anal. Appl., 36:2 (2002), 83–92

Citation in format AMSBIB
\by V.~I.~Arnol'd
\paper Optimization in Mean and Phase Transitions in Controlled Dynamical Systems
\jour Funktsional. Anal. i Prilozhen.
\yr 2002
\vol 36
\issue 2
\pages 1--11
\jour Funct. Anal. Appl.
\yr 2002
\vol 36
\issue 2
\pages 83--92

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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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