This paper introduces a novel hybrid method for solving a stochastic control problem for linear, Gaussian systems through uncertain environments. Due to the imperfect knowledge of the system state caused by motion, sensor and environment uncertainty, the system constraints cannot be guaranteed to be satisfied and consequently must be considered probabilistically. Due to the environmental uncertainty, the constraints are sums of products of random variables which do not have a closed-form analytical expression. Previous approaches have either approximated the distribution leading to a nonconvex optimization program, or used sampling alone to represent the uncertainty which requires a large number of samples to accurately represent the distribution. To address these limitations, a novel hybrid method is proposed that uses both analytical functions and sampling to represent the uncertainty. It is shown that under certain conditions, the resulting optimization program is convex. Also, this method drastically reduces the computational complexity over previous methods, which is demonstrated through an example.
