International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 72, Pages 4517-4538
doi:10.1155/S0161171203302108

On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost

Silvia C. Di Marco and Roberto L. V. González

 CONICET, Instituto de Matematica Beppo Levi, FCEIA, Universidad Nacional de Rosario, Pellegrini 250, Rosario 2000, Argentina
Received 11 February 2003

Abstract

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.