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Differential games with unbounded versus bounded controls. (English) Zbl 0909.90286

Summary: A zero-sum differential game with an unbounded control and no coercivity assumptions is investigated. By means of suitable reparametrization techniques one is able to avoid the serious drawbacks which derive from the lack of a sufficiently fast growth hypothesis. In particular, one achieves a remarkable regularization of the two related Hamilton-Jacobi boundary value problems. One also proves that the latter admit unique continuous solutions, which coincide necessarily with the upper and lower values of the game.

MSC:

91A23 Differential games (aspects of game theory)
49L20 Dynamic programming in optimal control and differential games
49N25 Impulsive optimal control problems
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
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