On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost - Silvia C. Di Marco; Roberto L. V. González (International Journal of Mathematics and Mathematical Sciences)
We study a minimax optimal control problem with finite horizon and additive final cost. After introducing an auxiliary problem, we analyze the dynamical programming principle (DPP) and we present a Hamilton-Jacobi-Bellman (HJB) system. We prove the existence and uniqueness of a viscosity solution for this system. This solution is the cost function of the auxiliary problem and it is possible to get the solution of the original problem in terms of this solution.