  This paper introduces a new formulation for stochastic optimal control and
stochastic dynamic optimization that ensures safety with respect to state and
control constraints. The proposed methodology brings together concepts such as
Forward-Backward Stochastic Differential Equations, Stochastic Barrier
Functions, Differentiable Convex Optimization and Deep Learning. Using the
aforementioned concepts, a Neural Network architecture is designed for safe
trajectory optimization in which learning can be performed in an end-to-end
fashion. Simulations are performed on three systems to show the efficacy of the
proposed methodology.
