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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 11, Pages 1843–1854 (Mi zvmmf219)  

This article is cited in 4 scientific papers (total in 4 papers)

Numerical method for solving a nonlinear time-optimal control problem with additive control

G. V. Shevchenko

Institute of Mathematics, Siberian Division, Russian Academy of Sciences, pr. Koptyuga 4, Novosibirsk, 630090, Russia

Abstract: Nonlinear systems whose right-hand sides are divided by the state and control and are linear in control are considered. An iterative method is proposed for solving time-optimal control problems for such systems. The method is based on constructing finite sequences of adjacent simplexes with their vertices lying on the boundaries of reachability sets. For a controllable system, it is proved that the minimizing sequence converges to an $\varepsilon$-optimal solution in a finite number of iterations.

Key words: nonlinear time-optimal control problem, numerical solution method.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:11, 1768–1778

Bibliographic databases:

UDC: 519.626
Received: 26.04.2006

Citation: G. V. Shevchenko, “Numerical method for solving a nonlinear time-optimal control problem with additive control”, Zh. Vychisl. Mat. Mat. Fiz., 47:11 (2007), 1843–1854; Comput. Math. Math. Phys., 47:11 (2007), 1768–1778

Citation in format AMSBIB
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\paper Numerical method for solving a~nonlinear time-optimal control problem with additive control
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\jour Comput. Math. Math. Phys.
\yr 2007
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. V. Shevchenko, “Numerical solution of a nonlinear time-optimal control problem”, Comput. Math. Math. Phys., 51:4 (2011), 537–549  mathnet  crossref  mathscinet  isi
    2. Grigorieva E.V., Khailov E.N., Korobeinikov A., “Parametrization of the Attainable Set for a Nonlinear Control Model of a Biochemical Process”, Math. Biosci. Eng., 10:4 (2013), 1067–1094  crossref  mathscinet  zmath  isi  elib  scopus
    3. 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
    4. Grigorieva E.V., Bondarenko N.V., Khailov E.N., “Time Optimal Control Problem For the Waste Water Biotreatment Model”, J. Dyn. Control Syst., 21:1 (2015), 3–24  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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