"**Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs**
Marcus Pereira (Georgia Institute Technology)*; Ziyi Wang (Georgia Institute of Technology); Ioannis Exarchos (Stanford University); Evangelos Theodorou (Georgia Institute of Technology)
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. "