Differential games and Zubov's method

L. Grüne, O.S.Serea: Differential games and Zubov's method
SIAM Journal on Control and Optimization 49 (6), 2349 - 2377, 2011

DOI: 10.1137/100787829
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Abstract:

In this paper we provide generalizations of Zubov's equation to differential games without Isaacs' condition. We show that both generalizations of Zubov's equation (which we call min-max and max-min Zubov equation, respectively) possess unique viscosity solutions which characterize the respective controllability domains. As a consequence, we show that under the usual Isaacs condition the respective controllability domains as well as the local controllability assumptions coincide

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