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Mat. Sb. (N.S.), 1981, Volume 116(158), Number 1(9), Pages 136–144 (Mi msb2447)  

This article is cited in 22 scientific papers (total in 22 papers)

On the alternating integral of Pontryagin

M. S. Nikol'skii

Abstract: Pontryagin introduced the notion of alternating integral to solve linear differential games of pursuit. To construct this integral one uses, in particular, Riemann integration of certain multivalued mappings.
Pontryagin posed the problem of constructing an alternating integral in such a way that the operation of integrating multivalued mappings is absent. One of the possible methods of such a construction is presented in this paper.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1983, 44:1, 125–132

Bibliographic databases:

UDC: 519.9
MSC: Primary 28B20; Secondary 90D25, 90D26
Received: 08.09.1980

Citation: M. S. Nikol'skii, “On the alternating integral of Pontryagin”, Mat. Sb. (N.S.), 116(158):1(9) (1981), 136–144; Math. USSR-Sb., 44:1 (1983), 125–132

Citation in format AMSBIB
\by M.~S.~Nikol'skii
\paper On the alternating integral of Pontryagin
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 1(9)
\pages 136--144
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 1
\pages 125--132

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    This publication is cited in the following articles:
    1. M. S. Nikol'skii, “On the lower alternating integral of Pontryagin in linear differential games of pursuit”, Math. USSR-Sb., 56:1 (1987), 33–47  mathnet  crossref  mathscinet  zmath
    2. Silin D., “On Set-Valued Differentiation and Integration”, Set-Valued Anal., 5:2 (1997), 107–146  crossref  mathscinet  zmath  isi
    3. A. A. Azamov, Kh. K. Yakhshimov, “Problem of quality for a certain linear differential game with critical properties”, Math. Notes, 67:4 (2000), 413–416  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Dar'in, AN, “Control under indeterminacy and double constraints”, Differential Equations, 39:11 (2003), 1554  mathnet  crossref  mathscinet  zmath  isi  elib
    5. S. I. Kumkov, V. S. Patsko, S. G. Pyatko, A. A. Fedotov, “Construction of the solvability set in a problem of guiding an aircraft under wind disturbance”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 1, S163–S174  mathnet  mathscinet  zmath  elib
    6. V. N. Ushakov, Ya. A. Latushkin, “Coincidence Criteria for Maximal Stable Bridges in Two Game Problems of Approach”, Proc. Steklov Inst. Math., 262 (2008), 244–262  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    7. V. N. Ushakov, Kh. G. Guseinov, Ya. A. Latushkin, P. D. Lebedev, “On the coincidence of maximal stable bridges in two approach game problems for stationary control systems”, Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S240–S263  mathnet  crossref  isi  elib
    8. Vladimir N. Ushakov, Aleksandr A. Uspenskii, “Defekt funktsii v differentsialnykh igrakh s terminalnoi platoi”, MTIP, 2:2 (2010), 99–128  mathnet  elib
    9. V. N. Ushakov, A. R. Matviichuk, P. D. Lebedev, “Defekt stabilnosti v igrovoi zadache o sblizhenii v moment”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 3, 87–103  mathnet  elib
    10. V. N. Ushakov, A. A. Uspenskii, “On a supplement to the stability property in differential games”, Proc. Steklov Inst. Math., 271 (2010), 286–305  mathnet  crossref  mathscinet  isi  elib
    11. Ushakov V.N., “K svoistvu stabilnosti v igrovoi zadache o sblizhenii s fiksirovannym momentom okonchaniya”, Differentsialnye uravneniya, 47:7 (2011), 1034–1046  mathscinet  zmath  elib
    12. V. N. Ushakov, P. D. Lebedev, A. R. Matviychuk, A. G. Malev, “Differential games with fixed terminal time and estimation of the instability degree of sets in these games”, Proc. Steklov Inst. Math., 277 (2012), 266–277  mathnet  crossref  mathscinet  isi  elib  elib
    13. Iskanadjiev I., “Duality of the Alternating Integral for Quasi-Linear Differential Games”, Nonlinear Anal.-Model Control, 17:2 (2012), 169–181  crossref  mathscinet  zmath  isi
    14. Iskanadjiev I.M., “On the Pontryagin Lower Alternating Integral”, J. Automat. Inf. Sci., 45:2 (2013), 33–40  crossref  isi
    15. S.S.. Kumkov, Stéphane Le Ménec, V.S.. Patsko, “Level Sets of the Value Function in Differential Games with Two Pursuers and One Evader. Interval Analysis Interpretation”, Math.Comput.Sci, 2014  crossref  mathscinet
    16. V. N. Ushakov, V. I. Ukhobotov, A. V. Ushakov, G. V. Parshikov, “On solving approach problems for control systems”, Proc. Steklov Inst. Math., 291 (2015), 263–278  mathnet  crossref  crossref  isi  elib
    17. Iskanadjiev I.M., “Lower Pontryagin'S Alternating Integral For Differential Inclusions”, Cybern. Syst. Anal., 51:5 (2015), 782–791  crossref  mathscinet  zmath  isi
    18. V. N. Ushakov, A. A. Ershov, “K resheniyu zadach upravleniya s fiksirovannym momentom okonchaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:4 (2016), 543–564  mathnet  crossref  mathscinet  elib
    19. A. A. Ershov, V. N. Ushakov, “An approach problem for a control system with an unknown parameter”, Sb. Math., 208:9 (2017), 1312–1352  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    20. Kumkov S.S. Le Menec S. Patsko V.S., “Zero-Sum Pursuit-Evasion Differential Games With Many Objects: Survey of Publications”, Dyn. Games Appl., 7:4, SI (2017), 609–633  crossref  mathscinet  zmath  isi  scopus
    21. V. N. Ushakov, V. I. Ukhobotov, A. E. Lipin, “An Addition to the Definition of a Stable Bridge and an Approximating System of Sets in Differential Games”, Proc. Steklov Inst. Math., 304 (2019), 268–280  mathnet  crossref  crossref  isi  elib
    22. N. G. Novoselova, N. N. Subbotina, “Postroenie mnozhestva vyzhivaemosti v zadache khimioterapii zlokachestvennoi opukholi, rastuschei po zakonu Gompertsa”, Tr. IMM UrO RAN, 26, no. 1, 2020, 173–181  mathnet  crossref  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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