Funktsional'nyi Analiz i ego Prilozheniya
General information
Latest issue
Impact factor
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Funktsional. Anal. i Prilozhen.:

Personal entry:
Save password
Forgotten password?

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


Full text: PDF file (160 kB)
References: PDF file   HTML file

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

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Vershik, “Random metric spaces and universality”, Russian Math. Surveys, 59:2 (2004), 259–295  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. A. A. Davydov, “Generic Profit Singularities in Arnold's Model of Cyclic Processes”, Proc. Steklov Inst. Math., 250 (2005), 70–84  mathnet  mathscinet  zmath
    3. Moreira, CS, “Singularities of the stationary domain for polydynamical systems”, Control and Cybernetics, 35:4 (2006), 881  mathscinet  zmath  isi
    4. A. A. Davydov, H. Mena Matos, “Generic phase transitions and profit singularities in Arnol'd's model”, Sb. Math., 198:1 (2007), 17–37  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. “Vladimir Igorevich Arnol'd (on his 70th birthday)”, Russian Math. Surveys, 62:5 (2007), 1021–1030  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. S. M. Aseev, A. V. Kryazhimskii, “The Pontryagin Maximum Principle and Optimal Economic Growth Problems”, Proc. Steklov Inst. Math., 257 (2007), 1–255  mathnet  crossref  mathscinet  zmath  elib
    7. Mena-Matos, H, “Generic singularities of the optimal averaged profit among stationary strategies”, Journal of Dynamical and Control Systems, 13:4 (2007), 541  crossref  mathscinet  zmath  isi  scopus
    8. Davydov A., Mena-Matos H., “Singularity theory approach to time averaged optimization”, Singularities in Geometry and Topology, 2005, 2007, 598–628  crossref  mathscinet  zmath  isi
    9. Davydov, AA, “Typical profit singularities of one-parametric cyclic process with fixed period”, Optimization, 57:2 (2008), 205  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. A. A. Davydov, T. S. Shutkina, “Optimizing a cyclic process with discount with respect to its time average profit”, Russian Math. Surveys, 64:1 (2009), 136–138  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Mena-Matos, H, “Generic profit singularities in time averaged optimization. The case of a control space with a regular boundary”, Journal of Dynamical and Control Systems, 16:1 (2010), 101  crossref  mathscinet  zmath  isi  scopus
    12. A. A. Davydov, T. S. Shutkina, “Optimizatsiya tsiklicheskikh protsessov s diskontirovaniem po usiliyu i vygode”, Nelineinaya dinam., 6:1 (2010), 151–158  mathnet  elib
    13. A. A. Davydov, T. S. Shutkina, “Uniqueness of a cycle with discounting that is optimal with respect to the average time profit”, Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S80–S87  mathnet  crossref  isi  elib
    14. A. A. Davydov, H. Mena-Matos, C. S. Moreira, “Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems”, Journal of Mathematical Sciences, 199:5 (2014), 510–534  mathnet  crossref  mathscinet
    15. Vysokii V.A., “Infrastrukturnye predposylki ekonomicheskoi aktivnosti”, Nauchnye issledovaniya i razrabotki. ekonomika firmy, 2 (2013), 82–92  elib
    16. 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  crossref  mathscinet  zmath  isi  scopus
    17. A. Belyakov, A. A. Davydov, “Efficiency optimization for the cyclic use of a renewable resource”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 14–21  mathnet  crossref  crossref  mathscinet  isi  elib
    18. Nikolay A. Krasovskii, Alexander M. Tarasyev, “Equilibrium trajectories in dynamical bimatrix games with average integral payoff functionals”, Autom. Remote Control, 79:6 (2018), 1148–1167  mathnet  crossref  isi
    19. N. A. Krasovskii, A. M. Tarasev, “Asimptoticheskoe povedenie reshenii v dinamicheskikh bimatrichnykh igrakh s diskontirovannymi indeksami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 193–209  mathnet  crossref  elib
    20. A. A. Davydov, “Existence of Optimal Stationary States of Exploited Populations with Diffusion”, Proc. Steklov Inst. Math., 310 (2020), 124–130  mathnet  crossref  crossref  mathscinet  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:1088
    Full text:443
    First page:6

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021