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Avtomatika i Telemekhanika, 2011, Issue 3, Pages 36–50 (Mi at1488)  
This article is cited in 22 scientific papers (total in 22 papers)

Nonlinear Systems

Degenerate problems of optimal control. I

V. I. Gurmana, Ni Ming Kangb

a Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalesskii, Russia
b East China Normal University, Shanghai, China
Full-text PDF (255 kB) Citations (22)
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Abstract: Considered is the practically important and theoretically challenging class of optimal control problems which can be integrated within the common notion of “degenerate problems”. The general definition of such problems is given, which arises from the connection between the degeneracy and the presence of hidden passive differential constraints or discrete chains in the problem. This definition is analyzed with the focus on its relation with the classical notion of degeneracy in the variational calculus and the notion of singular and sliding modes well known in the control theory. This paper is the first one in the series of three, which are aimed at presenting a survey of the main facts and applications of the special theory of such problems, which is essentially based on finding and eliminating passive constraints. New results and generalizations are also reported.
Presented by the member of Editorial Board: E. Ya. Rubinovich

Received: 18.03.2010
English version:
Automation and Remote Control, 2011, Volume 72, Issue 3, Pages 497–511
DOI: https://doi.org/10.1134/S0005117911030039
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. I. Gurman, Ni Ming Kang, “Degenerate problems of optimal control. I”, Avtomat. i Telemekh., 2011, no. 3, 36–50; Autom. Remote Control, 72:3 (2011), 497–511
Citation in format AMSBIB
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    Cycle of papers
    This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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