Stochastic Optimal Control for Nonlinear Systems based on Sampling & Deep Learning

Stochastic optimal control requires an adequate representation of state uncertainty. For stochastic nonlinear systems, the probability distribution over the states given measurements can often not be represented in closed form. In this paper, we thus propose to address this control task based on Monte-Carlo sampling, integrating the state estimation step with stochastic gradient descent-based control optimisation. A deep neural network approximation of the nonlinear system is the key to speeding up both parts. We motivate and demonstrate the approach for district heating systems, where the security of supply shall be guaranteed with high probability in the face of uncertain consumer demands. Our conceptually simple approach enables representing multimodal distributions and achieving computation times feasible for the online operation of district heating systems.