Abstract:
The paper is devoted to the time-optimal problem for three- and four-dimensional nonlinear control systems with one-dimensional control. We obtain sufficient conditions for a time-optimal control to be equivalent (in the Lebesgue sense) to a piecewise constant control that is also optimal, has a finite number of discontinuity points, and takes only extreme values. Such optimal controls are called bang-bang solutions and are of considerable interest in control theory and its applications.
Citation:
M. S. Nikol'skii, “On the time-optimal problem for three- and four-dimensional control systems”, Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 277, MAIK Nauka/Interperiodica, Moscow, 2012, 192–198; Proc. Steklov Inst. Math., 277 (2012), 184–190
\Bibitem{Nik12}
\by M.~S.~Nikol'skii
\paper On the time-optimal problem for three- and four-dimensional control systems
\inbook Mathematical control theory and differential equations
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2012
\vol 277
\pages 192--198
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3393}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3052272}
\elib{https://elibrary.ru/item.asp?id=17759406}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 277
\pages 184--190
\crossref{https://doi.org/10.1134/S008154381204013X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000309232900013}
Linking options:
https://www.mathnet.ru/eng/tm3393
https://www.mathnet.ru/eng/tm/v277/p192
This publication is cited in the following 3 articles:
Vetchinkin A.S., Starichenkov A.L., “Formati on of the Trajectory of Convergence of Marine Mobile Objects”, Mar. Intellect. Technol., 2020, no. 1, 1, 113–117
Vetchinkin A.S., Starichenkov A.L., “Minimum Time Control of the Course of the Ship, Taking Into Account the Limitations For the Variation of Value and Speed of Change of the Control Response”, Mar. Intellect. Technol., 4:4 (2018), 191–196
Andrei Korobeinikov, Evgenii Khailov, Ellina Grigorieva, Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015, 549
Citation in format AMSBIB
Contact us: