Ural Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Ural Math. J.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Ural Mathematical Journal, 2016, Volume 2, Issue 1, Pages 58–68
DOI: https://doi.org/10.15826/umj.2016.1.006 (Mi umj15) 		 
On the structure of singular set of a piecewise smooth minimax solution of Hamilton-Jacobi-Bellman equation

Aleksei S. Rodinab

a Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
b Ural Federal University, Ekaterinburg, Russia
Full-text PDF (172 kB)
References:
PDF
HTML
DOI: https://doi.org/10.15826/umj.2016.1.006
Abstract: The properties of a minimax piecewise smooth solution of the Hamilton-Jacobi-Bellman equation are studied. We get a generalization of the nesessary and sufficient conditions for the points of nondifferentiability (singularity) of the minimax solution and the Rankine-Hugoniot condition. We describe the dimensions of smooth manifolds containing in the singular set of the piecewise smooth solution in terms of state characteristics crossing on this singular set. New structural properties of the singular set are obtained for the case of the Hamiltonian depending only on the impulse variable.
Keywords: Hamilton-Jacobi-Bellman equation, Minimax solution, Singular set, Piecewise smooth solution, Tangent subspace, Rankine-Hugoniot condition.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00168
Russian Academy of Sciences - Federal Agency for Scientific Organizations 387-2015-0075
1This work was supported by the Russian Foundation for Basic Research (project no. 14-01-00168) and by the Program of the Presidium of the Russian Academy of Sciences “Mathematical Problems of Contemporary Control Theory”(project no. 387-2015-0075).
Bibliographic databases:
Document Type: Article
Language: English
Citation: Aleksei S. Rodin, “On the structure of singular set of a piecewise smooth minimax solution of Hamilton-Jacobi-Bellman equation”, Ural Math. J., 2:1 (2016), 58–68
Citation in format AMSBIB
\Bibitem{Rod16}
\by Aleksei~S.~Rodin
\paper On the structure of singular set of a piecewise smooth minimax solution of Hamilton-Jacobi-Bellman equation
\jour Ural Math. J.
\yr 2016
\vol 2
\issue 1
\pages 58--68
\mathnet{http://mi.mathnet.ru/umj15}
\crossref{https://doi.org/10.15826/umj.2016.1.006}
\zmath{https://zbmath.org/?q=an:1413.35133}
\elib{https://elibrary.ru/item.asp?id=26501483}
Linking options:
  • https://www.mathnet.ru/eng/umj15
  • https://www.mathnet.ru/eng/umj/v2/i1/p58
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Ural Mathematical Journal
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024