  The majority of methods used to compute approximations to the
Hamilton-Jacobi-Isaacs partial differential equation (HJI PDE) rely on the
discretization of the state space to perform dynamic programming updates. This
type of approach is known to suffer from the curse of dimensionality due to the
exponential growth in grid points with the state dimension. In this work we
present an approximate dynamic programming algorithm that computes an
approximation of the solution of the HJI PDE by alternating between solving a
regression problem and solving a minimax problem using a feedforward neural
network as the function approximator. We find that this method requires less
memory to run and to store the approximation than traditional gridding methods,
and we test it on a few systems of two, three and six dimensions.
