RBM-MPC

This is the code we used for the numerical experiments with RBM-MPC, a combination of Model Predictive Control (MPC) and Random Batch Methods (RBMs). There are three critical parameters that need to be tuned in RBM-MPC, the prediction horizon $T$, the control horizon $\tau$, and the time scale of the randomization $h$. The RBM-MPC algorithm is applied to control a heat equation with periodic boundary conditions with is discretized by finite differences with $n$ spatial grid points. The code in this repository has been used to generate the numerical examples in the paper TODO.

The file C0_basic_code computes one realization of an RBM-MPC trajectory. The files C1_multiple_realizations, C2_varyh, C3_varyT, C4_varytau, and C5_varyn compute multiple realizations and show the influence of the parameters that define the RBM-MPC strategy.