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Mat. Teor. Igr Pril., 2011, Volume 3, Issue 1, Pages 91–117 (Mi mgta55)  

This article is cited in 13 scientific papers (total in 13 papers)

On Volterra functional operator games on a given set

Andrey V. Chernov

Institute of Radioelectronics and Information Technology, Nizhnii Novgorod State Technical University

Abstract: The paper is devoted to obtaining the sufficient conditions of $\varepsilon$-equilibrium in the sense of piecewise program strategies in antagonistic games associated with nonlinear controlled functional operator equations and cost functional of a general enough form. The concept of piecewise program strategies is defined on the base of a concept of Volterra set chain for operators involved in the equations controlled by the opponent players. The reduction of controlled distributed parameter systems to an equation of the type under study is illustrated by examples.

Keywords: functional operator game, nonlinear functional operator equations, Volterra set chain, piecewise program strategies, $\varepsilon$-equilibrium.

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English version:
Automation and Remote Control, 2014, 75:4, 787–803

Bibliographic databases:

UDC: 517.988+517.977.8
BBK: 22.18

Citation: Andrey V. Chernov, “On Volterra functional operator games on a given set”, Mat. Teor. Igr Pril., 3:1 (2011), 91–117; Autom. Remote Control, 75:4 (2014), 787–803

Citation in format AMSBIB
\by Andrey~V.~Chernov
\paper On Volterra functional operator games on a~given set
\jour Mat. Teor. Igr Pril.
\yr 2011
\vol 3
\issue 1
\pages 91--117
\jour Autom. Remote Control
\yr 2014
\vol 75
\issue 4
\pages 787--803

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    This publication is cited in the following articles:
    1. Andrei V. Chernov, “O suschestvovanii $\varepsilon$-ravnovesiya v volterrovykh funktsionalno-operatornykh igrakh bez diskriminatsii”, MTIP, 4:1 (2012), 74–92  mathnet
    2. A. V. Chernov, “O volterrovom obobschenii metoda monotonizatsii dlya nelineinykh funktsionalno-operatornykh uravnenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 2, 84–99  mathnet  elib
    3. A. V. Chernov, “K issledovaniyu zavisimosti resheniya upravlyaemogo funktsionalno-operatornogo uravneniya ot sdviga upravleniya”, Izv. IMI UdGU, 2012, no. 1(39), 157–158  mathnet
    4. A. V. Chernov, “Sufficient conditions for the controllability of nonlinear distributed systems”, Comput. Math. Math. Phys., 52:8 (2012), 1115–1127  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    5. A. V. Chernov, “Ob $\varepsilon$-ravnovesii v beskoalitsionnykh funktsionalno-operatornykh igrakh so mnogimi uchastnikami”, Tr. IMM UrO RAN, 19, no. 1, 2013, 316–328  mathnet  mathscinet  elib
    6. A. V. Chernov, “Ob upravlyaemosti nelineinykh raspredelennykh sistem na mnozhestve konechnomernykh approksimatsii upravleniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 1, 83–98  mathnet
    7. Andrei V. Chernov, “Ob odnom podkhode k postroeniyu $\varepsilon$-ravnovesiya v beskoalitsionnykh igrakh, svyazannykh s uravneniyami matematicheskoi fiziki, upravlyaemykh mnogimi igrokami”, MTIP, 5:1 (2013), 104–123  mathnet
    8. Andrei V. Chernov, “O suschestvovanii $\varepsilon$-ravnovesiya v differentsialnykh igrakh, svyazannykh s ellipticheskimi uravneniyami, upravlyaemymi mnogimi igrokami”, MTIP, 6:1 (2014), 91–115  mathnet
    9. Chernov A.V., “On the Convexity of Reachability Sets of Controlled Initial-Boundary Value Problems”, Differ. Equ., 50:5 (2014), 700–710  crossref  mathscinet  zmath  isi  elib  scopus
    10. A. V. Chernov, “On convexity local conditions for attainable tubes of controlled distributed systems”, Russian Math. (Iz. VUZ), 58:11 (2014), 60–73  mathnet  crossref
    11. A. V. Chernov, “O totalno globalnoi razreshimosti upravlyaemogo uravneniya tipa Gammershteina s variruemym lineinym operatorom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:2 (2015), 230–243  mathnet  elib
    12. Andrei V. Chernov, “O suschestvovanii ravnovesiya po Neshu v differentsialnoi igre, svyazannoi s ellipticheskimi uravneniyami: monotonnyi sluchai”, MTIP, 7:3 (2015), 48–78  mathnet
    13. A. V. Chernov, “Ob analoge teoremy Uintnera dlya upravlyaemogo ellipticheskogo uravneniya”, Izv. IMI UdGU, 2015, no. 2(46), 228–235  mathnet  elib
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