Differential Games and Zubov's Method

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Grüne, Lars ; Serea, Oana Silvia:
Differential Games and Zubov's Method.
Bayreuth , 2011

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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.