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Isaacs’ equations for value-functions of differential games. (English) Zbl 0770.90093
Optimization, optimal control and partial differential equations. Proc. 1st Fr.-Rom. Conf., Iasi/Rom. 1992, ISNM 107, 193-206 (1992).
Summary: [For the entire collection see Zbl 0752.00054.]
We study value functions of a differential game with payoff which depends on the state at a given end time. We consider differential games with feedback strategies and with nonanticipating strategies. We prove that value-functions are solutions to some Hamilton-Jacobi-Isaacs equations in the viscosity and contingent sense. For these two notions of strategies, with some regularity assumptions, we prove that value-functions are the unique solution of Isaacs’ equations.

91A23 Differential games (aspects of game theory)
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games