  In this paper we present an information theoretic approach to stochastic
optimal control problems for systems with compound Poisson noise. We generalize
previous work on information theoretic path integral control to discontinuous
dynamics with compound Poisson noise and develop an iterative model predictive
control (MPC) algorithm using importance sampling. The proposed algorithm is
parallelizable and when implemented on a Graphical Processing Unit (GPU) can
run in real time. We test the performance of the proposed algorithm in
simulation for two control tasks using a cartpole system and a quadrotor. Our
simulations demonstrate improved performance of the new scheme and indicate the
importance of incorporating the statistical characteristics of stochastic
disturbances in the computation of the stochastic optimal control policies.
