In this work we deal with the numerical solution of a Hamilton-Jacobi-Bellman (HJB) equation with infinitely many solutions. To compute the maximal solution – the optimal cost of the original optimal control problem – we present a complete discrete method based on the use of some finite elements and penalization techniques.
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...
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