  In this paper, we propose a new methodology for state constrained stochastic
optimal control (SOC) problems. The solution is based on past work in solving
SOC problems using forward-backward stochastic differential equations (FBSDE).
Our approach in solving the FBSDE utilizes a deep neural network (DNN),
specifically Long Short-Term Memory (LSTM) networks. LSTMs are chosen to solve
the FBSDE to address the curse of dimensionality, non-linearities, and long
time horizons. In addition, the state constraints are incorporated using a hard
penalty function, resulting in a controller that respects the constraint
boundaries. Numerical instability that would be introduced by the penalty
function is dealt with through an adaptive update scheme. The control design
methodology is applicable to a large class of control problems. The performance
and scalability of our proposed algorithm are demonstrated by numerical
simulations.
