Information Theoretic Model Predictive Control on Jump Diffusion Processes

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. We also derive a control update law of the same form using a stochastic optimization approach. We develop a sampling-based iterative model predictive control (MPC) algorithm. 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 and a quadrotor system. 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.