Does the effort of Monte Carlo pay off? A case study on stochastic MPC

Abstract Stochastic Model Predictive Control (MPC) has established itself as a simple method to approximate stochastically disturbed optimal control problems, yet it comes with significant computational effort. In particular, taking into account all information of stochastic disturbances—if at all possible—can be expensive. However, due to the continuous re-optimization, MPC schemes also have a certain inherent robustness. Hence, we ask the question, which part of the perturbation is absorbed by the MPC-inherent robustness, and which needs to be explicitly taken into account in the optimization. In this paper, we compare several stochastic MPC algorithms taking into account a growing amount of the stochastic information: starting with deterministic schemes of certainty equivalence type, we use the noise’s distribution’s quantiles and finally we take, potentially, all stochastic information into account when performing Monte Carlo simulations in the MPC scheme. We carry out a numerical case study for the inverted pendulum, in which we observe that for short prediction horizons Monte Carlo does not pay off while for large prediction horizon it has slight advantages. Further, we discuss possible explanations for this behavior.