Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2014, Issue 2, Pages 84–92
This article is cited in 1 scientific paper (total in 1 paper)
Viscosity solutions and programmed iteration method for Isaacs equation
F. F. Nikitin
St. Petersburg State University, 199034, St. Petersburg, Russia Federation
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.
zero-sum differential games, viscosity solutions, Isaacs equation, programmed iteration method, value operators, value of differential game.
PDF file (256 kB)
Received: December 19, 2013
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
\paper Viscosity solutions and programmed iteration method for Isaacs equation
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
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
|Number of views:|