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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 4, Pages 868–885 (Mi izv1278)  

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

Abstract: An analytic solution of a time-optimal problem for the oscillatory system
$$ \dot{x}=Ax+bu,\qquad|u|\leqslant1,\quad\operatorname{rank}(b,Ab,…,A^{n-1}b)=n, $$
is given, where the spectrum $\sigma(A)=\{\pm ik\lambda,k=0,1,…,p;\lambda>0\}$. 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.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:1, 203–220

Bibliographic databases:

UDC: 517.977
MSC: Primary 49E30; Secondary 42A70
Received: 24.12.1987

Citation: V. I. Korobov, G. M. Sklyar, “Time-optimal control and the trigonometric moment problem”, Izv. Akad. Nauk SSSR Ser. Mat., 53:4 (1989), 868–885; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 4
\pages 868--885
\mathnet{http://mi.mathnet.ru/izv1278}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1018752}
\zmath{https://zbmath.org/?q=an:0706.49005}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 1
\pages 203--220
\crossref{https://doi.org/10.1070/IM1990v035n01ABEH000696}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. V. Shevchenko, “Numerical method for solving a nonlinear time-optimal control problem with additive control”, Comput. Math. Math. Phys., 47:11 (2007), 1768–1778  mathnet  crossref  mathscinet  elib  elib
    2. K. S. Khalina, “Controllability problems for the non-homogeneous string that is fixed at the right-end point with Dirichlet boundary control at the left point”, Zhurn. matem. fiz., anal., geom., 7:1 (2011), 34–58  mathnet  mathscinet  zmath  elib
    3. K. S. Khalina, “On the Neumann boundary controllability for the non-homogeneous string on a segment”, Zhurn. matem. fiz., anal., geom., 7:4 (2011), 333–351  mathnet  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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