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Mathematics of the USSR-Izvestiya, 1990, Volume 35, Issue 1, Pages 203–220
DOI: https://doi.org/10.1070/IM1990v035n01ABEH000696
(Mi im1278)
 

This article is cited in 3 scientific papers (total in 3 papers)

Time-optimal control and the trigonometric moment problem

V. I. Korobov, G. M. Sklyar

Kharkiv State University
References:
Abstract: An analytic solution of a time-optimal problem for the oscillatory system
$$ \dot{x}=Ax+bu,\qquad|u|\leqslant1,\quad\operatorname{rank}(b,Ab,\dots,A^{n-1}b)=n, $$
is given, where the spectrum $\sigma(A)=\{\pm ik\lambda,k=0,1,\dots,p;\lambda>0\}$. Introducing a special system of trigonometric polynomials (canonical variables) and studying Toeplitz determinants in these variables, the authors obtain equations for determining the control time, as well as the points and surfaces of switching the optimal control. The solution thus obtained is, on the other hand, the solution of a trigonometric moment problem on the smallest possible interval in the form of a function of a $(-1,1)$-moment sequence. The question of local equivalence of linear time-optimal problems is considered for systems with a one-dimensional control.
Bibliography: 6 titles.
Received: 24.12.1987
Bibliographic databases:
UDC: 517.977
MSC: Primary 49E30; Secondary 42A70
Language: English
Original paper language: Russian
Citation: V. I. Korobov, G. M. Sklyar, “Time-optimal control and the trigonometric moment problem”, Math. USSR-Izv., 35:1 (1990), 203–220
Citation in format AMSBIB
\Bibitem{KorSkl89}
\by V.~I.~Korobov, G.~M.~Sklyar
\paper Time-optimal control and the trigonometric moment problem
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 1
\pages 203--220
\mathnet{http://mi.mathnet.ru//eng/im1278}
\crossref{https://doi.org/10.1070/IM1990v035n01ABEH000696}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1018752}
\zmath{https://zbmath.org/?q=an:0706.49005}
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  • https://doi.org/10.1070/IM1990v035n01ABEH000696
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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