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Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 2, Pages 275–284 (Mi timm953)  

This article is cited in 11 scientific papers (total in 11 papers)

A method for constructing a resolving control in an approach problem based on attraction to the solvability set

V. N. Ushakov, A. R. Matviychuk, G. V. Parshikov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The problem of approach of a nonlinear control system to a compact target set in the phase space at a fixed time is studied. An algorithm for constructing a solution of this problem based on maximum attraction of the system's motion to the solvability set is proposed.

Keywords: control system, game problem of approach, reachable set, solvability set, integral funnel, invariance, weak invariance.

Full text: PDF file (168 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 284, suppl. 1, 135–144

Bibliographic databases:

UDC: 517.977.1
Received: 20.11.2012

Citation: V. N. Ushakov, A. R. Matviychuk, G. V. Parshikov, “A method for constructing a resolving control in an approach problem based on attraction to the solvability set”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 2, 2013, 275–284; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 135–144

Citation in format AMSBIB
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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. Ushakov V.N., Ushakov V A., Parshikov V G., “One Method of Attraction To the Solvability Set in the Convergence Problem”, Applications of Mathematics in Engineering and Economics (AMEE'14), AIP Conf. Proc., 1631, eds. Venkov G., Pasheva V., Amer. Inst. Phys., 2014, 209–217  crossref  isi  scopus
    2. V. N. Ushakov, A. R. Matviichuk, “K resheniyu zadach upravleniya nelineinymi sistemami na konechnom promezhutke vremeni”, Izv. IMI UdGU, 2015, no. 2(46), 202–215  mathnet  elib
    3. V. N. Ushakov, G. V. Parshikov, A. R. Matviychuk, “On some questions in computer modeling of the reachability sets constructing problems”, Application of Mathematics in Technical and Natural Sciences (AMITANS'16), AIP Conf. Proc., 1773, ed. M. Todorov, Amer. Inst. Phys., 2016, 110015  crossref  isi  scopus
    4. G. V. Parshikov, “O priblizhennom vychislenii mnozhestva razreshimosti v zadache o sblizhenii statsionarnoi upravlyaemoi sistemy na konechnom promezhutke vremeni”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 210–221  mathnet  crossref  elib
    5. G. V. Parshikov, A. R. Matviychuk, “On resource-efficient algorithm for non-linear systems approximate reachability set construction”, Application of Mathematics in Technical and Natural Sciences, AIP Conf. Proc., 1895, ed. M. Todorov, Amer. Inst. Phys., 2017, UNSP 120007-1  crossref  isi  scopus
    6. A. R. Matviychuk, V. I. Ukhobotov, A. V. Ushakov, V. N. Ushakov, “The approach problem of a nonlinear controlled system in a finite time interval”, J. Appl. Math. Mech., 81:2 (2017), 114–128  crossref  mathscinet  isi  scopus
    7. V. N. Ushakov, V. I. Ukhobotov, A. R. Matviychuk, G. V. Parshikov, “On some nonlinear control system problems on a finite time interval”, IFAC-PapersOnLine, 51:32 (2018), 832–837  crossref  mathscinet  isi  scopus
    8. V. N. Ushakov, V. I. Ukhobotov, A. V. Ushakov, G. V. Parshikov, “On game approach problems on a finite time interval”, International Conference of Computational Methods in Sciences and Engineering 2018 (ICCMSE-2018), AIP Conference Proceedings, 2040, eds. T. Simos, Z. Kalogiratou, T. Monovasilis, Amer. Inst. Physics, 2018, 050003  crossref  isi
    9. V. N. Ushakov, A. A. Ershov, “On recovering of unknown constant parameter by several test controls”, Ufa Math. J., 12:4 (2020), 99–113  mathnet  crossref  isi
    10. A. A. Zimovets, A. R. Matviichuk, “Setochnyi algoritm postroeniya mnozhestv dostizhimosti s uluchshennoi approksimatsiei granitsy”, Chelyab. fiz.-matem. zhurn., 6:1 (2021), 9–21  mathnet  crossref
    11. V. N. Ushakov, A. V. Ushakov, O. A. Kuvshinov, “O konstruirovanii razreshayuschego upravleniya v zadache o sblizhenii v fiksirovannyi moment vremeni”, Izv. IMI UdGU, 58 (2021), 73–93  mathnet  crossref
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