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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 2, Pages 1–11
DOI: https://doi.org/10.4213/faa186 (Mi faa186) 		 
This article is cited in 31 scientific papers (total in 32 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
Full-text PDF (160 kB) Citations (32)
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DOI: https://doi.org/10.4213/faa186
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.
Received: 14.11.2001
English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 2, Pages 83–92
DOI: https://doi.org/10.1023/A:1015655005114
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
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
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    • This publication is cited in the following 32 articles:
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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