Sequential Convex Programming For Non-Linear Stochastic Optimal Control

We introduce a sequential convex programming framework to solve general non-linear stochastic optimal control problems in finite dimension, where uncertainties are modeled by a multidimensional Wiener process. We provide sufficient conditions for the convergence of the method. Moreover, we prove that, when convergence is achieved, sequential convex programming finds a candidate locally optimal solution for the original problem in the sense of the stochastic Pontryagin Maximum Principle. We leverage those properties to design a practical numerical method to solve non-linear stochastic optimal control problems that is based on a deterministic transcription of stochastic sequential convex programming.