We study the target problem which is a differential game where one of the players aims at reaching a target while the other player aims at avoiding this target forever. We characterize the victory domains of the players by means of geometric conditions and prove that the boundary of the victory domains is a nonsmooth semipermeable surface, i.e., is a solution (in a weak sense) of the Isaacs equation: sup u inf v 〈 f ( x, u, v ), p 〉 = 0, where f is the dynamic of the system, u and v are the respective controls of the players, and p is a normal to the boundary of the victory domains at the point x .
Applied Mathematics and Optimization – Springer Journals
Published: Sep 1, 1997
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