RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






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


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 2, Pages 162–177 (Mi vuu578)  

MATHEMATICS

Regularization of the Pontryagin maximum principle in the problem of optimal boundary control for a parabolic equation with state constraints in Lebesgue spaces

A. A. Gorshkov, M. I. Sumin

Lobachevsky State University of Nizhni Novgorod, pr. Gagarina, 23, Nizhni Novgorod, 603950, Russia

Abstract: A convex optimal control problem is considered for a parabolic equation with a strictly uniformly convex cost functional, with boundary control and distributed pointwise state constraints of equality and inequality type. The images of the operators that define pointwise state constraints are embedded into the Lebesgue space of integrable with $s$-th degree functions for $s\in(1,2)$. In turn, the boundary control belongs to Lebesgue space with summability index $r\in (2,+\infty)$. The main results of this work in the considered optimal control problem with pointwise state constraints are the two stable, with respect to perturbation of input data, sequential or, in other words, regularized principles: Lagrange principle in nondifferential form and Pontryagin maximum principle.

Keywords: optimal boundary control, parabolic equation, sequential optimization, dual regularization, stability, pointwise state constraint in the Lebesgue space, Lagrange principle, Pontryagin's maximum principle.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-47-02294-р_поволжье_а
Ministry of Education and Science of the Russian Federation 1727


DOI: https://doi.org/10.20537/vm170202

Full text: PDF file (341 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 517.97
MSC: 47A52
Received: 10.11.2016

Citation: A. A. Gorshkov, M. I. Sumin, “Regularization of the Pontryagin maximum principle in the problem of optimal boundary control for a parabolic equation with state constraints in Lebesgue spaces”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:2 (2017), 162–177

Citation in format AMSBIB
\Bibitem{GorSum17}
\by A.~A.~Gorshkov, M.~I.~Sumin
\paper Regularization of the Pontryagin maximum principle in the problem of optimal boundary control for a parabolic equation with state constraints in Lebesgue spaces
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 2
\pages 162--177
\mathnet{http://mi.mathnet.ru/vuu578}
\crossref{https://doi.org/10.20537/vm170202}
\elib{http://elibrary.ru/item.asp?id=29410189}


Linking options:
  • http://mi.mathnet.ru/eng/vuu578
  • http://mi.mathnet.ru/eng/vuu/v27/i2/p162

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:2030
    Full text:27
    References:22

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019