  Solving high dimensional optimal control problems and corresponding
Hamilton-Jacobi PDEs are important but challenging problems in control
engineering. In this paper, we propose two abstract neural network
architectures which are respectively used to compute the value function and the
optimal control for certain class of high dimensional optimal control problems.
We provide the mathematical analysis for the two abstract architectures. We
also show several numerical results computed using the deep neural network
implementations of these abstract architectures. A preliminary implementation
of our proposed neural network architecture on FPGAs shows promising speed up
compared to CPUs. This work paves the way to leverage efficient dedicated
hardware designed for neural networks to solve high dimensional optimal control
problems and Hamilton-Jacobi PDEs.
