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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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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
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\issue 1
\pages 91--117
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\transl
\jour Autom. Remote Control
\yr 2014
\vol 75
\issue 4
\pages 787--803
\crossref{https://doi.org/10.1134/S0005117914040195}
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http://mi.mathnet.ru/eng/mgta55 http://mi.mathnet.ru/eng/mgta/v3/i1/p91
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This publication is cited in the following articles:
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Andrei V. Chernov, “O suschestvovanii $\varepsilon$-ravnovesiya v volterrovykh funktsionalno-operatornykh igrakh bez diskriminatsii”, MTIP, 4:1 (2012), 74–92
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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
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A. V. Chernov, “K issledovaniyu zavisimosti resheniya upravlyaemogo funktsionalno-operatornogo uravneniya ot sdviga upravleniya”, Izv. IMI UdGU, 2012, no. 1(39), 157–158
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A. V. Chernov, “Sufficient conditions for the controllability of nonlinear distributed systems”, Comput. Math. Math. Phys., 52:8 (2012), 1115–1127
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A. V. Chernov, “Ob $\varepsilon$-ravnovesii v beskoalitsionnykh funktsionalno-operatornykh igrakh so mnogimi uchastnikami”, Tr. IMM UrO RAN, 19, no. 1, 2013, 316–328
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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
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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
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Andrei V. Chernov, “O suschestvovanii $\varepsilon$-ravnovesiya v differentsialnykh igrakh, svyazannykh s ellipticheskimi uravneniyami, upravlyaemymi mnogimi igrokami”, MTIP, 6:1 (2014), 91–115
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Chernov A.V., “On the Convexity of Reachability Sets of Controlled Initial-Boundary Value Problems”, Differ. Equ., 50:5 (2014), 700–710
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A. V. Chernov, “On convexity local conditions for attainable tubes of controlled distributed systems”, Russian Math. (Iz. VUZ), 58:11 (2014), 60–73
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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
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Andrei V. Chernov, “O suschestvovanii ravnovesiya po Neshu v differentsialnoi igre, svyazannoi s ellipticheskimi uravneniyami: monotonnyi sluchai”, MTIP, 7:3 (2015), 48–78
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A. V. Chernov, “Ob analoge teoremy Uintnera dlya upravlyaemogo ellipticheskogo uravneniya”, Izv. IMI UdGU, 2015, no. 2(46), 228–235
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