Fast, Convexified Stochastic Optimal Open-Loop Control for Linear Systems Using Empirical Characteristic Functions

We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of characteristic functions and underapproximating cumulative distribution functions, we can reformulate a nonconvex problem by a conic, convex under-approximation. This results in extremely fast solutions that are assured to maintain probabilistic constraints. We construct algorithms to solve an optimal open-loop control problem and demonstrate our approach on two examples.