Convexified Open-Loop Stochastic Optimal Control for Linear Systems With Log-Concave Disturbances

Abstract

We consider open-loop solutions to the stochastic optimal control of a linear dynamical system with an additive non-Gaussian, log-concave disturbance. We propose a novel, sampling-free approach, based on characteristic functions and convex optimization, to cast the stochastic optimal control problem as a difference-of-convex program. Our method invokes higher moments, resulting in less conservatism compared to moment-based approaches. We employ piecewise affine approximations and the convex-concave procedure for efficient solution via standard conic solvers. We demonstrate that the proposed solution is competitive with sampling and moment based approaches, without compromising probabilistic constraints.