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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






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


Trudy Inst. Mat. i Mekh. UrO RAN, 2019, Volume 25, Number 3, Pages 163–170 (Mi timm1656)  

Estimation of reachable sets from above with respect to inclusion for some nonlinear control systems

M. S. Nikol'skii

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The study of reachable sets of controlled objects is an important research area in optimal control theory. Such sets describe in a rough form the dynamical possibilities of the objects, which is important for theory and applications. Many optimization problems for controlled objects use the reachable set $D(T)$ in their statements. In the study of properties of controlled objects, it is useful to have some constructive estimates of $D(T)$ from above with respect to inclusion. In particular, such estimates are helpful for the approximate calculation of $D(T)$ by the pixel method. In this paper we consider two nonlinear models of direct regulation known in the theory of absolute stability with a control term added to the right-hand side of the corresponding system of differential equations. To obtain the required upper estimates with respect to inclusion, we use Lyapunov functions from the theory of absolute stability. Note that the upper estimates for $D(T)$ are obtained in the form of balls in the phase space centered at the origin.

Keywords: reachable set, Lyapunov function, absolute stability, direct regulation.

DOI: https://doi.org/10.21538/0134-4889-2019-25-3-163-170

Full text: PDF file (173 kB)
First page: PDF file
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.977
MSC: 42C10, 47A58
Received: 04.04.2019
Revised: 16.04.2019
Accepted:29.04.2019

Citation: M. S. Nikol'skii, “Estimation of reachable sets from above with respect to inclusion for some nonlinear control systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 3, 2019, 163–170

Citation in format AMSBIB
\Bibitem{Nik19}
\by M.~S.~Nikol'skii
\paper Estimation of reachable sets from above with respect to inclusion for some nonlinear control systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 3
\pages 163--170
\mathnet{http://mi.mathnet.ru/timm1656}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-3-163-170}
\elib{http://elibrary.ru/item.asp?id=39323546}


Linking options:
  • http://mi.mathnet.ru/eng/timm1656
  • http://mi.mathnet.ru/eng/timm/v25/i3/p163

    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
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Number of views:
    This page:12
    References:3
    First page:2

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