The value of a minimax problem involving impulse control (Q2274614)

The paper addresses a deterministic minimax control problem in finite horizon. In this model, there are two players; namely, player 1 uses an instantaneous control that applies through time in order to maximize his/her gain denoted by \(J\). In contrast, player 2 uses an impulse-type control and his/her aim is to minimize \(J\). Under suitable conditions, the optimal value of this problem is charactarized as a unique viscosity solution of a certain nonlinear quasi-variational inequality. All the proofs are well written and with rigorous details.