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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 2, Pages 100–105 (Mi vuu325)  

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Computational solution of time-optimal control problem for linear systems with delay

G. V. Shevchenko

Laboratory of Differential and Difference Equations, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: A computational method of solving time-optimal control problem for linear systems with delay is proposed. It is proved that the method converges in a finite number of iterations to an $\varepsilon$-optimal solution, which is understood as a pair $\{T,u\},$ where $u=u(t)$, $t\in[0,T]$ is an admissible control that moves the system into an $\varepsilon$-neighborhood of the origin in time $T\le T_{\min}$, and the optimal time is $T_{\min}$. An enough general time-optimal control problem with delay is studied in [Vasil'ev F. P, Ivanov R. P. On an approximated solving of time-optimal control problem with delay, Zh. Vychisl. Mat. Mat. Fiz., 1970, vol. 10, no. 5, pp. 1124–1140 (in Russian)], an approximate solution is proposed for it, and computational aspects are discussed. However, to solve some auxiliary optimal control problems arising there, it is suggested to use methods of gradient and Newton type, which possess only a local convergence. The method proposed in the present paper has a global convergence.

Keywords: admissible control, optimal control, time-optimal control.

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Document Type: Article
UDC: 517.97
MSC: 49J15, 49M05
Received: 20.02.2012

Citation: G. V. Shevchenko, “Computational solution of time-optimal control problem for linear systems with delay”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 2, 100–105

Citation in format AMSBIB
\Bibitem{She12}
\by G.~V.~Shevchenko
\paper Computational solution of time-optimal control problem for linear systems with delay
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 2
\pages 100--105
\mathnet{http://mi.mathnet.ru/vuu325}


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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, “A numerical method to minimize resource consumption by linear systems with constant delay”, Autom. Remote Control, 75:10 (2014), 1732–1742  mathnet  crossref  isi
    2. V. P. Maksimov, “Ob odnom klasse zadach optimalnogo upravleniya dlya funktsionalno-differentsialnykh sistem”, Vypusk posvyaschen 70-letnemu yubileyu Aleksandra Georgievicha Chentsova, Tr. IMM UrO RAN, 24, no. 1, 2018, 131–142  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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