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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, Issue 4, Pages 23–39 (Mi vuu294)  

This article is cited in 17 scientific papers (total in 17 papers)


Approximations of attainability sets and of integral funnels of differential inclusions

V. N. Ushakov, A. R. Matviichuk, A. V. Ushakov

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

Abstract: The paper is devoted to differential inclusions (DI) on finite time intervals. We consider some questions of computation of attainable sets for DI. The above sets are rarely describable analytically in an effective way though, often, there is a necessity for their computation, for example, in control theory, in which the above computation is a stimulus to develop methods and algorithms used to approximately compute attainable sets.

Keywords: attainability sets, integral funnel, differential inclusion.

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UDC: 517.977.5
MSC: 35F15, 37G10
Received: 12.10.2011

Citation: V. N. Ushakov, A. R. Matviichuk, A. V. Ushakov, “Approximations of attainability sets and of integral funnels of differential inclusions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 4, 23–39

Citation in format AMSBIB
\by V.~N.~Ushakov, A.~R.~Matviichuk, A.~V.~Ushakov
\paper Approximations of attainability sets and of integral funnels of differential inclusions
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 4
\pages 23--39

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    This publication is cited in the following articles:
    1. A. R. Matviichuk, P. D. Lebedev, A. V. Ushakov, “O priblizhennom postroenii mnozhestv dostizhimosti upravlyaemykh sistem na konechnom promezhutke vremeni”, Izv. IMI UdGU, 2012, no. 1(39), 94–94  mathnet
    2. V. N. Ushakov, A. A. Uspenskii, “Defekt stabilnosti deformatsii maksimalnogo stabilnogo mosta dlya igrovoi zadachi sblizheniya s zamknutoi tselyu”, Izv. IMI UdGU, 2012, no. 1(39), 140–140  mathnet
    3. A. V. Ushakov, “Ob odnom variante priblizhennogo postroeniya razreshayuschikh upravlenii v zadache o sblizhenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 94–107  mathnet
    4. V. N. Ushakov, A. R. Matviichuk, A. V. Ushakov, A. L. Kazakov, “O postroenii reshenii zadachi o sblizhenii v fiksirovannyi moment vremeni”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:4 (2012), 95–115  mathnet
    5. V. N. Ushakov, A. R. Matviichuk, A. V. Ushakov, G. V. Parshikov, “Invariantnost mnozhestv pri konstruirovanii reshenii zadachi o sblizhenii v fiksirovannyi moment vremeni”, Tr. IMM UrO RAN, 19, no. 1, 2013, 264–283  mathnet  mathscinet  elib
    6. 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”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 135–144  mathnet  crossref  mathscinet  isi  elib
    7. V. N. Ushakov, N. G. Lavrov, A. V. Ushakov, “Konstruirovanie reshenii v zadache o sblizhenii statsionarnoi upravlyaemoi sistemy”, Tr. IMM UrO RAN, 20, no. 4, 2014, 277–286  mathnet  mathscinet  elib
    8. Ushakov V., Matviychuk A., Brykalov S., “Invariance Property in Approaching Problem on a Finite Time Interval”, Large-Scale Scientific Computing, Lssc 2013, Lecture Notes in Computer Science, 8353, eds. Lirkov I., Margenov S., Wasniewski J., Springer-Verlag Berlin, 2014, 152–158  crossref  mathscinet  isi  scopus
    9. A. Yu. Gornov, E. A. Finkel'shtein, “Algorithm for piecewise-linear approximation of the reachable set boundary”, Autom. Remote Control, 76:3 (2015), 385–393  mathnet  crossref  isi  elib  elib
    10. Vladimir N. Ushakov, Sergey A. Brykalov, Grigory V. Parshikov, “$\alpha$-systems of differential inclusions and their unification”, Autom. Remote Control, 77:8 (2016), 1480–1499  mathnet  crossref  isi
    11. A. A. Zimovets, A. R. Matviichuk, “Parallelnyi algoritm priblizhennogo postroeniya mnozhestv dostizhimosti nelineinykh upravlyaemykh sistem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:4 (2015), 459–472  mathnet  elib
    12. 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
    13. V. N. Zhermolenko, A. S. Poznyak, “Necessary and sufficient conditions for stabilizability of planar parametrically perturbed control systems”, IMA J. Math. Control Inf., 33:1 (2016), 53–68  crossref  mathscinet  zmath  isi  elib  scopus
    14. A. Yu. Gornov, T. S. Zarodnyuk, E. A. Finkelstein, A. S. Anikin, “The method of uniform monotonous approximation of the reachable set border for a controllable system”, J. Glob. Optim., 66:1, SI (2016), 53–64  crossref  mathscinet  zmath  isi  scopus
    15. V. N. Ushakov, S. A. Brykalov, G. V. Parshikov, “A guidance problem for a differential inclusion with parameter”, Dokl. Math., 93:3 (2016), 289–291  crossref  mathscinet  zmath  isi  elib  elib  scopus
    16. T. F. Filippova, “External estimates for reachable sets of a control system with uncertainty and combined nonlinearity”, Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 32–43  mathnet  crossref  crossref  isi  elib
    17. Parshikov G.V., Matviychuk A.R., “On Resource-Efficient Algorithm For Non-Linear Systems Approximate Reachability Set Construction”, AIP Conference Proceedings, 1895, ed. Todorov M., Amer Inst Physics, 2017, UNSP 120007-1  crossref  isi  scopus
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