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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2012, Volume 15, Number 1, Pages 1–19 (Mi sjvm454)  
This article is cited in 6 scientific papers (total in 6 papers)

Forming an approximating construction for calculation and implementation of optimal control in real time

V. M. Aleksandrov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (307 kB) Citations (6)
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Abstract: A new approach to realization of the time-optimal control in real time for linear systems under control with a constraint is proposed. It is based on dividing the computer costs into those made in advance of the control process and those carried out as it proceeds. The preliminary computations do not depend on certain initial condition and rely on approximation of attainability sets in different periods of time by a union of hyperplanes. Methods of their construction and singling out the support hyperplane are given. Methods of approximate finding and subsequent correction of the normalized vector of the initial conditions of the conjugate system as well as switching times and instants of switching of time-optimal control are proposed. Results of modeling and numerical calculations are presented.
Key words: optimal control, attainability sets, hyperplane, real time, adjoint system, edge point, first approximation, approximating construction.
Received: 25.03.2011
English version:
Numerical Analysis and Applications, 2012, Volume 5, Issue 1, Pages 1–16
DOI: https://doi.org/10.1134/S1995423912010016
Bibliographic databases:
Document Type: Article
UDC: 519.626.1
Language: Russian
Citation: V. M. Aleksandrov, “Forming an approximating construction for calculation and implementation of optimal control in real time”, Sib. Zh. Vychisl. Mat., 15:1 (2012), 1–19; Num. Anal. Appl., 5:1 (2012), 1–16
Citation in format AMSBIB
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\paper Forming an approximating construction for calculation and implementation of optimal control in real time
\jour Sib. Zh. Vychisl. Mat.
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\vol 15
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\pages 1--19
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\elib{https://elibrary.ru/item.asp?id=17979270}
\transl
\jour Num. Anal. Appl.
\yr 2012
\vol 5
\issue 1
\pages 1--16
\crossref{https://doi.org/10.1134/S1995423912010016}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84857891966}
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  • https://www.mathnet.ru/eng/sjvm454
  • https://www.mathnet.ru/eng/sjvm/v15/i1/p1
    • This publication is cited in the following 6 articles:
    1. V. M. Aleksandrov, “Real-time computation of resource optimal control”, Comput. Math. Math. Phys., 59:7 (2019), 1074–1084  mathnet  crossref  crossref  isi  elib
    2. V. M. Aleksandrov, “Computing of optimal inertial control with a linear system”, Num. Anal. Appl., 8:1 (2015), 1–12  mathnet  crossref  mathscinet  elib
    3. V. M. Aleksandrov, “Zadanie nachalnogo priblizheniya i metod vychisleniya optimalnogo upravleniya”, Sib. elektron. matem. izv., 11 (2014), 87–118  mathnet
    4. V. M. Aleksandrov, “A method of optimal real-time computation of a linear system with retarded control”, Num. Anal. Appl., 7:1 (2014), 15–25  mathnet  crossref  mathscinet  isi
    5. V. M. Aleksandrov, “Transferring a system with unknown disturbance under optimal control to a state of dynamic balance and to $\epsilon$-vicinity of a final state”, Num. Anal. Appl., 6:2 (2013), 119–130  mathnet  crossref  mathscinet  elib
    6. V. M. Aleksandrov, “Optimalnoe upravlenie dinamicheskoi sistemoi pri nepolnoi informatsii”, Sib. elektron. matem. izv., 9 (2012), 329–345  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Sibirskii Zhurnal Vychislitel'noi Matematiki
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    Abstract page:463
    Full-text PDF :119
    References:91
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