
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 2, Pages 100–105
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This article is cited in 2 scientific papers (total in 2 papers)
MATHEMATICS
Computational solution of timeoptimal 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 timeoptimal 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 timeoptimal control problem with delay is studied in [Vasil'ev F. P, Ivanov R. P. On an approximated solving of timeoptimal 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, timeoptimal control.
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UDC:
517.97
MSC: 49J15, 49M05 Received: 20.02.2012
Citation:
G. V. Shevchenko, “Computational solution of timeoptimal 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 timeoptimal control problem for linear systems with delay
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 2
\pages 100105
\mathnet{http://mi.mathnet.ru/vuu325}
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This publication is cited in the following articles:

G. V. Shevchenko, “A numerical method to minimize resource consumption by linear systems with constant delay”, Autom. Remote Control, 75:10 (2014), 1732–1742

V. P. Maksimov, “On a class of optimal control problems for functional differential systems”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S114–S124

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