Trudy Instituta Matematiki i Mekhaniki UrO RAN
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 Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 2, Pages 73–86 (Mi timm1172)  

This article is cited in 19 scientific papers (total in 19 papers)

Positional strengthenings of the maximum principle and sufficient optimality conditions

V. A. Dykhta

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk
References:
Abstract: We derive nonlocal necessary optimality conditions, which efficiently strengthen the classical Pontryagin maximum principle and its modification obtained by B.Kaskosz and S.Lojasiewicz as well as our previous result of a similar kind named the “feedback minimum principle”. The strengthening of the feedback minimum principle (and, hence, of the Pontryagin principle) is owing to the employment of two types of feedback controls “compatible” with a reference trajectory (i.e., producing this trajectory as a Caratheodory solution). In each of the versions, the strengthened feedback minimum principle states that the optimality of a reference process implies the optimality of its trajectory in a certain family of variational problems generated by adjoint trajectories of the original and compatible controls. The basic construction of the feedback minimum principle - a perturbation of a solution to the adjoint system - is employed to prove an exact formula for the increment of the cost functional. We use this formula to obtain sufficient conditions for the strong and global minimum of Pontryagin's extremals. These conditions are much milder than their known analogs, which require the convexity in the state variable of the functional and of the lower Hamiltonian. Our study is focused on a nonlinear smooth Mayer problem with free terminal states. All assertions are illustrated by examples.
Keywords: maximum principle, extremal, adjoint trajectory, necessary and sufficient conditions, feedback controls.
Received: 16.02.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 293, Issue 1, Pages 43–57
DOI: https://doi.org/10.1134/S0081543816050059
Bibliographic databases:
Document Type: Article
UDC: 517.977.5
Language: Russian
Citation: V. A. Dykhta, “Positional strengthenings of the maximum principle and sufficient optimality conditions”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 73–86; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 43–57
Citation in format AMSBIB
\Bibitem{Dyk15}
\by V.~A.~Dykhta
\paper Positional strengthenings of the maximum principle and sufficient optimality conditions
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 2
\pages 73--86
\mathnet{http://mi.mathnet.ru/timm1172}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3408880}
\elib{https://elibrary.ru/item.asp?id=23607922}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 293
\issue , suppl. 1
\pages 43--57
\crossref{https://doi.org/10.1134/S0081543816050059}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000380005200005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84978472861}
Linking options:
  • https://www.mathnet.ru/eng/timm1172
  • https://www.mathnet.ru/eng/timm/v21/i2/p73
  • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Statistics & downloads:
    Abstract page:390
    Full-text PDF :108
    References:66
    First page:13
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024