Minimax optimal control problems. Numerical analysis of the finite horizon case

Abstract

In this paper we consider the numerical computation of the optimal cost function associated to the problem that consists in finding the minimum of the maximum of a scalar functional on a trajectory. We present an approximation method for the numerical solution which employs both discretization on time and on spatial variables. In this way, we obtain a fully discrete problem that has unique solution. We give an optimal estimate for the error between the approximated solution and the optimal cost function of the original problem. Also, numerical examples are presented.