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Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2014, Issue 2, Pages 84–92 (Mi vspui188)  

This article is cited in 1 scientific paper (total in 1 paper)

Applied mathematics

Viscosity solutions and programmed iteration method for Isaacs equation

F. F. Nikitin

St. Petersburg State University, 199034, St. Petersburg, Russia Federation

Abstract: To solve zero-sum differential games Isaacs derived PDE of Hamilton–Jacobi type for value function. However, in many differential games the value function is not smooth. The theory of viscosity solutions overcomes non-smoothness of the value function by introducing generalized solutions of PDE. Programmed iteration method considers functional equation for the value function which is called generalized Isaacs–Bellman equation. In the paper connection between the theory of viscosity solutions and programmed iteration method is studied. It turns out that successive approximations utilized in programmed iteration method for finding solutions of generalized Isaacs–Bellman equation and any fixed point of value operators are corresponding viscosity super or sub-solutions of Isaacs equation. Bibliogr. 24.

Keywords: zero-sum differential games, viscosity solutions, Isaacs equation, programmed iteration method, value operators, value of differential game.

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UDC: 519.837.4, 517.977.8
Received: December 19, 2013
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Citation: F. F. Nikitin, “Viscosity solutions and programmed iteration method for Isaacs equation”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2014, no. 2, 84–92

Citation in format AMSBIB
\Bibitem{Nik14}
\by F.~F.~Nikitin
\paper Viscosity solutions and programmed iteration method for Isaacs equation
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2014
\issue 2
\pages 84--92
\mathnet{http://mi.mathnet.ru/vspui188}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Chistyakov, “Ob uravneniyakh metoda programmnykh iteratsii”, Vypusk posvyaschen 70-letnemu yubileyu Aleksandra Georgievicha Chentsova, Tr. IMM UrO RAN, 24, no. 1, 2018, 288–296  mathnet  crossref  elib
  • Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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