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Avtomat. i Telemekh., 2011, Issue 9, Pages 127–141 (Mi at2280)  

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

Topical issue

Algorithms to estimate the reachability sets of the pulse controlled systems with ellipsoidal phase constraints

T. F. Filippova, O. G. Matviichuk

Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

Abstract: Methods to construct the ellipsoidal estimates of the reachability sets of a nonlinear dynamic system with scalar pulse control and uncertainty in the initial data were proposed. The considered pulse system was rearranged in the ordinary differential inclusion already without any pulse components by means of a special discontinuous time substitution. The results of the theory of ellipsoidal estimation and the theory of evolutionary equations of the multivalued states of dynamic systems under uncertainty and ellipsoidal phase constraints were used to estimate the reachability sets of the resulting nonlinear differential inclusion.

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English version:
Automation and Remote Control, 2011, 72:9, 1911–1924

Bibliographic databases:

Document Type: Article
Presented by the member of Editorial Board: L. B. Rapoport

Received: 12.04.2011

Citation: T. F. Filippova, O. G. Matviichuk, “Algorithms to estimate the reachability sets of the pulse controlled systems with ellipsoidal phase constraints”, Avtomat. i Telemekh., 2011, no. 9, 127–141; Autom. Remote Control, 72:9 (2011), 1911–1924

Citation in format AMSBIB
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\pages 1911--1924
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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. Matviychuk O.G., “Estimation Problem for Impulsive Control Systems Under Ellipsoidal State Bounds and with Cone Constraint on the Control”, Applications of Mathematics in Engineering and Economics (AMEE'12), AIP Conference Proceedings, 1497, eds. Pasheva V., Venkov G., Amer Inst Physics, 2012, 3–12  crossref  adsnasa  isi  scopus
    2. E. K. Kostousova, “On the polyhedral method of solving problems of control strategy synthesis”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 140–155  mathnet  crossref  mathscinet  isi  elib
    3. Matviychuk O.G., “Internal Ellipsoidal Estimates of Reachable Set of Impulsive Control Systems”, Applications of Mathematics in Engineering and Economics (AMEE'14), AIP Conference Proceedings, 1631, eds. Venkov G., Pasheva V., Amer Inst Physics, 2014, 238–244  crossref  isi  scopus
    4. Matviychuk O.G., “Internal Ellipsoidal Estimates of Reachable Set of Impulsive Control Systems Under Ellipsoidal State Bounds and With Cone Constraint on the Control”, Large-Scale Scientific Computing, Lssc 2013, Lecture Notes in Computer Science, 8353, eds. Lirkov I., Margenov S., Wasniewski J., Springer-Verlag Berlin, 2014, 125–132  crossref  mathscinet  isi  scopus
    5. Tatiana F. Filippova, Oksana G. Matviychuk, “Estimates of reachable sets of control systems with bilinear-quadratic nonlinearities”, Ural Math. J., 1:1 (2015), 45–54  mathnet  crossref
    6. Matviychuk O.G., “Internal Ellipsoidal Estimates For Bilinear Systems Under Uncertainty”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conference Proceedings, 1789, eds. Pasheva V., Popivanov N., Venkov G., Amer Inst Physics, 2016, UNSP 060008  crossref  isi  scopus
    7. Filippova T.F., “Estimates of Reachable Sets of Impulsive Control Problems With Special Nonlinearity”, Application of Mathematics in Technical and Natural Sciences (Amitans'16), AIP Conference Proceedings, 1773, ed. Todorov M., Amer Inst Physics, 2016, 100004  crossref  isi  scopus
    8. T. F. Filippova, “Vneshnie otsenki mnozhestv dostizhimosti upravlyaemoi sistemy s neopredelennostyu i kombinirovannoi nelineinostyu”, Tr. IMM UrO RAN, 23:1 (2017), 262–274  mathnet  crossref  elib
    9. T. F. Filippova, “Otsenki mnozhestv dostizhimosti sistem s impulsnym upravleniem, neopredelennostyu i nelineinostyu”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 205–216  mathnet  crossref
    10. Mikhail I. Gusev, “An algorithm for computing boundary points of reachable sets of control systems under integral constraints”, Ural Math. J., 3:1 (2017), 44–51  mathnet  crossref
    11. Matviychuk O.G., “Estimation Techniques For Bilinear Control Systems”, IFAC PAPERSONLINE, 51:32 (2018), 877–882  crossref  isi  scopus
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