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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 304, Pages 252–256
DOI: https://doi.org/10.4213/tm3970 (Mi tm3970) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Singular Sets of Extremal Controls in Optimal Control Problems

M. S. Nikol'skii

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
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DOI: https://doi.org/10.4213/tm3970
Abstract: Some optimal control problems are considered with an integral functional (to be minimized), fixed motion time of the controlled object, and free right endpoint. In these problems, the set of degeneracy points of the Pontryagin maximum principle (singular set) for the extremal control is studied. For a wide class of linear control systems, sufficient conditions are obtained under which the singular set is either empty or consists of a finite set of points. In addition, an example of a control system is constructed in which the singular set has a very general form.
Received: September 28, 2018
Revised: October 24, 2018
Accepted: December 24, 2018
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 304, Pages 236–240
DOI: https://doi.org/10.1134/S0081543819010164
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: M. S. Nikol'skii, “Singular Sets of Extremal Controls in Optimal Control Problems”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 252–256; Proc. Steklov Inst. Math., 304 (2019), 236–240
Citation in format AMSBIB
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\paper Singular Sets of Extremal Controls in Optimal Control Problems
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\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
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\vol 304
\pages 252--256
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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